Deck 9: Quadratic Equations, Inequalities, and Functions

Question 1

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $x^{2}+8 x+7=0$

A) $\{1,7\}$
B) $\{-7,0\}$
C) $\{0,7\}$
D) $\{-7,-1\}$

Answer 1

$\{-7,-1\}$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $x^{2}+2 x-15=0$

A) $\{5,3\}$
B) $\{-5,3\}$
C) $\{-3,5\}$
D) $\{-5,-3\}$

Answer 2

$\{-5,3\}$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $x^{2}+7 x+12=0$

A) $\{3,-4\}$
B) $\{-3,-4\}$
C) $\{3,4\}$
D) $\{-3,4\}$

Answer 3

$\{-3,-4\}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $2 x^{2}-14 x+24=0$

A) $\{3,4\}$
B) $\{-3,4\}$
C) $\{-4,3\}$
D) $\{-4,-3\}$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $3 x^{2}+x-44=0$

A) $\left\{-4,-\frac{11}{3}\right\}$

B) $\left\{-\frac{11}{3}, 4\right\}$

C) $\left\{-4, \frac{11}{3}\right\}$

D) $\left\{\frac{11}{3}, 4\right\}$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $7 x^{2}-41 x-6=0$

A) $\{-7,6\}$

B) $\left\{-\frac{1}{7}, 7\right\}$

C) $\left\{-\frac{1}{7}, 6\right\}$

D) $\left\{\frac{1}{41},-\frac{1}{7}\right\}$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $x^{2}=6 x-8$

A) $\{-8,-1\}$
B) $\{4,2\}$
C) $\{-4,-2\}$
D) $\{1,8\}$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation

- $2 x^{2}=-15 x-25$

A) $\{-5,-10\}$

B) $\left\{5, \frac{5}{2}\right\}$

C) $\left\{-\frac{5}{2},-5\right\}$

D) $\left\{5,-\frac{5}{2}\right\}$

Question 9

Use the square root property to solve the equation.

- $x^{2}=100$

A) $\{10\}$

B) $\{50\}$

C) $\{10,-10\}$

D) $\{11,-11\}$

Question 10

Use the square root property to solve the equation.

- $x^{2}-25=0$

A) $\{5,-5\}$

B) $\{13.5\}$

C) $\{5\}$

D) $\{4,-4\}$

Question 11

Use the square root property to solve the equation.

- $8 z^{2}-200=0$

A) $\{5\}$
B) $\{6,-6\}$
C) $\{5,-5\}$
D) $\{102.5\}$

Question 12

Use the square root property to solve the equation.

- $-5 k^{2}+20=0$

A) $\{-12.5\}$
B) $\{2,-2\}$
C) $\{2\}$
D) $\{4,-4\}$

Question 13

Use the square root property to solve the equation.

- $y^{2}=20$

A) $\{2 \sqrt{5},-2 \sqrt{5}\}$
B) $\{400\}$
C) $\{10\}$
D) $\{\sqrt{20}\}$

Question 14

Use the square root property to solve the equation.

- $(x+19)^{2}=36$

A) $\{-25,-13\}$
B) $\{25,13\}$
C) $\{-13\}$
D) $\{-55\}$

Question 15

Use the square root property to solve the equation.

- $(\mathrm{p}-2)^{2}=13$

A) $\{\sqrt{13}-2,-\sqrt{13-2}\}$
B) $\{2+\sqrt{13}, 2-\sqrt{13}\}$
C) $\{\sqrt{13}-\sqrt{-2}\}$
D) $\{2+\sqrt{13}\}$

Question 16

Use the square root property to solve the equation.

- $(3 s+9)^{2}=25$

A) $\left\{\frac{4}{3}, \frac{14}{3}\right\}$

B) $\left\{-\frac{4}{3}, 0\right\}$

C) $\left\{\frac{16}{3}\right\}$

D) $\left\{-\frac{4}{3},-\frac{14}{3}\right\}$

Question 17

Use the square root property to solve the equation.

- $(7 \mathrm{t}-3)^{2}=7$

A) $\left\{\frac{\sqrt{3}}{7} i,-\frac{\sqrt{3}}{7}\right\}$

B) $\left\{\frac{3+\sqrt{7}}{7}, \frac{3-\sqrt{7}}{7}\right\}$

C) $\left\{\frac{3-\sqrt{7}}{7},-\frac{3-\sqrt{7}}{7}\right\}$

D) $\{3+\sqrt{7}, 3-\sqrt{7}\}$

Question 18

Use the square root property to solve the equation.

- $(x+9)^{2}-6=0$

A) $\{-9+\mathrm{i} \sqrt{6},-9-\mathrm{i} \sqrt{6}\}$
B) $\{-3,15\}$
C) $\{-3+\sqrt{6},-3-\sqrt{6}\}$
D) $\{-9+\sqrt{6},-9-\sqrt{6}\}$

Question 19

Solve the problem using Galileo's formula, $d=16 t^{2}$ . Round your answer to the nearest tenth.

-Eric has a treehouse $27 \mathrm{ft}$ above the ground. How long would it take a water balloon dropped from the treehouse to fall to the ground?

A) $5.2 \mathrm{sec}$
B) $2.8 \mathrm{sec}$
C) $1.3 \mathrm{sec}$
D) $11,664 \mathrm{sec}$

Question 20

Solve the problem using Galileo's formula, $d=16 t^{2}$ . Round your answer to the nearest tenth.

-A young boy is delighted to drop various objects from a hotel balcony to the ground below. If he is $161 \mathrm{ft}$ above the ground, how long does it take for one of the objects to fall to the ground?

A) $161.0 \mathrm{sec}$
B) $10.1 \mathrm{sec}$
C) $12.7 \mathrm{sec}$
D) $3.2 \mathrm{sec}$

Question 21

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+8 x+$

A) $16 ;(x-4)^{2}$
B) $64 ;(x+8)^{2}$
C) $0 ;(x+4)^{2}$
D) $16 ;(x+4)^{2}$

Question 22

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+18 x+$

A) $81 ;(x-9)^{2}$
B) $81 ;(x+9)^{2}$
C) $324 ;(x+18)^{2}$
D) $0 ;(x+9)\}^{2}$

Question 23

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+5 x+$

A) $0 ;(x+5)^{2}$

B) $0 ;\left(x+\frac{5}{2}\right)^{2}$

C) $\frac{25}{4} ;\left(x+\frac{5}{2}\right)^{2}$

D) $\frac{25}{4} ;\left(x-\frac{5}{2}\right)^{2}$

Question 24

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-5 x+$

A) $\frac{25}{4} ;\left(x+\frac{5}{2}\right)^{2}$

B) $0 ;\left(x-\frac{5}{2}\right)^{2}$

C) $\frac{25}{4} ;\left(x-\frac{5}{2}\right)^{2}$

D) $25 ;(x-5)^{2}$

Question 25

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-\frac{2}{3} x+$

A) $9 ;\left(x-\frac{1}{3}\right)^{2}$

B) $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$

C) $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$

D) $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$

Question 26

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-\frac{5}{4} x+$

A) $0 ;\left(x-\frac{5}{8}\right)^{2}$

B) $\frac{25}{16} ;\left(x-\frac{5}{8}\right)^{2}$

C) $\frac{25}{64} ;\left(x+\frac{5}{8}\right)^{2}$

D) $\frac{25}{64} ;\left(x-\frac{5}{8}\right)^{2}$

Question 27

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve.

- $w^{2}-10 w-6=0$

A) 9
B) 25
C) -5
D) 0

Question 28

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve.

- $5 x^{2}+x-3=0$

A) $-\frac{1}{100}$
B) $\frac{1}{4}$
C) 100
D) $\frac{1}{100}$

Question 29

Solve the equation by completing the square.

- $a^{2}+8 a-33=0$

A) $\{-22,-11\}$
B) $\{3,-11\}$
C) $\{6,-6\}$
D) $\{-3,11\}$

Question 30

Solve the equation by completing the square.

- $\mathrm{z}^{2}+16 \mathrm{z}+52=0$

A) $\{8+2 \sqrt{3}\}$

B) $\{8+2 \sqrt{13}, 8-2 \sqrt{13}\}$

C) $\{-8+2 \sqrt{3},-8-2 \sqrt{3}\}$

D) $\{-16+2 \sqrt{13}\}$

Question 31

Solve the equation by completing the square.

- $\mathrm{p}^{2}+3 \mathrm{p}-9=0$

A) $\left\{\frac{3+3 \sqrt{5}}{2}\right\}$

B) $\left\{\frac{-3-3 \sqrt{5}}{2}\right\}$

C) $\left\{\frac{-3+3 \sqrt{5}}{2}, \frac{-3-3 \sqrt{5}}{2}\right\}$

D) $\{-3+3 \sqrt{5},-3-3 \sqrt{5}\}$

Question 32

Solve the equation by completing the square.

- $6 x^{2}+4 x-2=0$

A) $\{3,0\}$
B) $\left\{\frac{1}{3},-1\right\}$
C) $\{3,-1\}$
D) $\{3,1\}$

Question 33

Solve the equation by completing the square.

- $21 \mathrm{~d}^{2}+34 \mathrm{~d}+8=0$

A) $\left\{\frac{2}{7}, \frac{4}{3}\right\}$

B) $\left\{-\frac{2}{7},-\frac{4}{3}\right\}$

C) $\left\{\frac{7}{2}, \frac{3}{4}\right\}$

D) $\left\{-\frac{7}{2},-\frac{4}{3}\right\}$

Question 34

Solve the equation by completing the square.

- $4 m^{2}+15 m=0$

A) $\{0\}$

B) $\left\{\frac{15}{4},-\frac{15}{4}\right\}$

C) $\left\{-\frac{15}{4}, 0\right\}$

D) $\left\{\frac{15}{4}, 0\right\}$

Question 35

Solve the equation by completing the square.

- $3 x^{2}+8 x=-2$

A) $\left\{\frac{-8+\sqrt{10}}{3}, \frac{-8-\sqrt{10}}{3}\right\}$

B) $\left\{\frac{-4+\sqrt{10}}{6}, \frac{-4-\sqrt{10}}{6}\right\}$

C) $\left\{\frac{-4+\sqrt{22}}{3}, \frac{-4-\sqrt{22}}{3}\right\}$

D) $\left\{\frac{-4+\sqrt{10}}{3}, \frac{-4-\sqrt{10}}{3}\right\}$

Question 36

Solve the equation by completing the square.

- $2 n^{2}=-12 n-5$

A) $\left\{\frac{-6+\sqrt{46}}{2}, \frac{-6-\sqrt{46}}{2}\right\}$

B) $\left\{\frac{-6+\sqrt{26}}{4}, \frac{-6-\sqrt{26}}{4}\right\}$

C) $\left\{\frac{-6+\sqrt{26}}{2}, \frac{-6-\sqrt{26}}{2}\right\}$

D) $\left\{\frac{-12+\sqrt{26}}{2}, \frac{-12-\sqrt{26}}{2}\right\}$

Question 37

Solve the equation by completing the square.

- $4 \mathrm{r}^{2}+22 \mathrm{r}=-20$

A) $\left\{\frac{-11+\sqrt{41}}{8}, \frac{-11-\sqrt{41}}{8}\right\}$

B) $\left\{\frac{-11+\sqrt{41}}{4}, \frac{-11-\sqrt{41}}{4}\right\}$

C) $\left\{\frac{-11+\sqrt{201}}{4}, \frac{-11-\sqrt{201}}{4}\right\}$

D) $\left\{\frac{-22+\sqrt{41}}{4}, \frac{-22-\sqrt{41}}{4}\right\}$

Question 38

Solve the equation by completing the square.

- $0.7 \mathrm{~m}^{2}+0.8 \mathrm{~m}+0.2=0$

A) $\left\{\frac{-4+\sqrt{2}}{14}, \frac{-4-\sqrt{2}}{14}\right\}$

B) $\left\{\frac{-4+\sqrt{2}}{7}, \frac{-4-\sqrt{2}}{7}\right\}$

C) $\left\{\frac{-4+\sqrt{30}}{7}, \frac{-4-\sqrt{30}}{7}\right\}$

D) $\left\{\frac{-8+\sqrt{2}}{7}, \frac{-8-\sqrt{2}}{7}\right\}$

Question 39

Solve the equation by completing the square.

- $0.1 \mathrm{x}^{2}-0.2 \mathrm{x}-0.1=0$

A) $\{1+\sqrt{2}\}$
B) $\{1+\sqrt{2}, 1-\sqrt{2}\}$
C) $\{2-\sqrt{2}\}$
D) $\{2+\sqrt{2}, 2-\sqrt{2}\}$

Question 40

Find the nonreal complex solutions of the equation.

- $x^{2}-10 x+29=0$

A) $\{7,3\}$
B) $\{10+4 \mathrm{i}, 10-4 \mathrm{i}\}$
C) $\{5+2 \mathrm{i}, 5-2 \mathrm{i}\}$
D) $\{-5+2 \mathrm{i},-5-2 \mathrm{i}\}$

Question 41

Find the nonreal complex solutions of the equation.

- $\mathrm{x}^{2}+4 \mathrm{x}+20=0$

A) $\{2,-6\}$
B) $\{-2+2 \sqrt{5} i,-2-2 \sqrt{5} i\}$
C) $\{-2+4 \mathrm{i},-2-4 \mathrm{i}\}$
D) $\{2+4 \mathrm{i}, 2-4 \mathrm{i}\}$

Question 42

Find the nonreal complex solutions of the equation.

- $x^{2}+x+2=0$

A) $\left\{\frac{1+\sqrt{-7}}{2}, \frac{1-\sqrt{-7}}{2}\right\}$

B) $\left\{\frac{-1+\sqrt{-7}}{2}, \frac{-1-\sqrt{-7}}{2}\right\}$

C) $\left\{\frac{1+\mathrm{i} \sqrt{7}}{2}, \frac{1-\mathrm{i} \sqrt{7}}{2}\right\}$

D) $\left\{\frac{-1+\mathrm{i} \sqrt{7}}{2}, \frac{-1-\mathrm{i} \sqrt{7}}{2}\right\}$

Question 43

Find the nonreal complex solutions of the equation.

- $5 x^{2}-5 x+7=0$

A) $\left\{\frac{5+\sqrt{115}}{10}, \frac{5-\sqrt{115}}{10}\right\}$

B) $\left\{\frac{-5+\sqrt{115}}{10}, \frac{-5-\sqrt{115}}{10}\right\}$

C) $\left\{\frac{-5+\mathrm{i} \sqrt{115}}{10}, \frac{-5-\mathrm{i} \sqrt{115}}{10}\right\}$

D) $\left\{\frac{5+\mathrm{i} \sqrt{115}}{10}, \frac{5-\mathrm{i} \sqrt{115}}{10}\right\}$

Question 44

Find the nonreal complex solutions of the equation.

- $-5 x^{2}-4 x-4=0$

A) $\left\{\frac{2}{5},-\frac{6}{5}\right\}$

B) $\left\{\frac{-4+\mathrm{i} \sqrt{64}}{10}, \frac{-4-\mathrm{i} \sqrt{64}}{10}\right\}$

C) $\left\{\frac{-2+4 \mathrm{i}}{5}, \frac{-2-4 \mathrm{i}}{5}\right\}$

D) $\left\{\frac{2+4 \mathrm{i}}{5}, \frac{2-4 \mathrm{i}}{5}\right\}$

Question 45

Find the nonreal complex solutions of the equation.

- $6 x^{2}-7 x+5=0$

A) $\left\{\frac{7+\sqrt{71}}{12}, \frac{7-\sqrt{71}}{12}\right\}$

B) $\left\{\frac{-7+\mathrm{i} \sqrt{71}}{12}, \frac{-7-\mathrm{i} \sqrt{71}}{12}\right\}$

C) $\left\{\frac{7+i \sqrt{71}}{12}, \frac{7-i \sqrt{71}}{12}\right\}$

D) $\left\{\frac{-7+\sqrt{71}}{12}, \frac{-7-\sqrt{71}}{12}\right\}$

Question 46

Find the nonreal complex solutions of the equation.

- $9 x^{2}+5 x+5=0$

A) $\left\{\frac{-5+\mathrm{i} \sqrt{155}}{18}, \frac{-5-\mathrm{i} \sqrt{155}}{18}\right\}$

B) $\left\{\frac{5+\mathrm{i} \sqrt{155}}{9}, \frac{5-\mathrm{i} \sqrt{155}}{9}\right\}$

C) $\left\{\frac{-5+\mathrm{i} \sqrt{155}}{9}, \frac{-5-\mathrm{i} \sqrt{155}}{9}\right\}$

D) $\left\{\frac{5+\mathrm{i} \sqrt{155}}{18}, \frac{5-\mathrm{i} \sqrt{155}}{18}\right\}$

Question 47

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers.

- $x^{2}-b=0$

A) $\{b,-b\}$
B) $\{\sqrt{b}, \sqrt{-b}\}$
C) $\{b\}$
D) $\{\sqrt{b},-\sqrt{b}\}$

Question 48

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers.

- $x^{2}=121 b$

A) $\{-11 b, 11 b\}$
B) $\{\sqrt{11 b},-\sqrt{11 b}\}$
C) $\{-11 \mathrm{i} \sqrt{\mathrm{b}}, 11 \mathrm{i} \sqrt{\mathrm{b}}\}$
D) $\{-11 \sqrt{b}, 11 \sqrt{b}\}$

Question 49

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers.

- $25 x^{2}=64 a$

A) $\left\{\frac{-8 a}{5}, \frac{8 a}{5}\right\}$

B) $\left\{\frac{-8 \sqrt{a}}{5}, \frac{8 \sqrt{a}}{5}\right\}$

C) $\left\{\frac{-\sqrt{8 a}}{5}, \frac{\sqrt{8 a}}{5}\right\}$

D) $\left\{\frac{-64 \sqrt{a}}{25}, \frac{64 \sqrt{a}}{25}\right\}$

Question 50

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers.

- $(3 x-4 b)^{2}=7 a$

A) $\left\{\frac{\sqrt{16 b^{2}+7 a}}{9}, \frac{-\sqrt{16 b^{2}-7 a}}{9}\right\}$

B) $\left\{\frac{4 b+\sqrt{7 a}}{3}, \frac{4 b-\sqrt{7 a}}{3}\right\}$

C) $\left\{\frac{4 b+\sqrt{7 a}}{3} \cdot \frac{-\sqrt{4 b-7 a}}{3}\right\}$

D) $\left\{\frac{4 b+7 a}{3}, \frac{-4 b-7 a}{3}\right\}$

Question 51

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers.

- $\mathrm{x}^{2}-\mathrm{a}^{2}-25=0$

A) $\left\{\sqrt{a^{2}+25},-\sqrt{a^{2}-25}\right\}$

B) $\left\{\sqrt{a^{2}+25},-\sqrt{a^{2}+25}\right\}$

C) $\left\{a^{2}+25, a^{2}-25\right\}$

D) $\left\{\sqrt{a^{2}+5},-\sqrt{a^{2}-5}\right\}$

Question 52

Define the term "quadratic equation".

Question 53

What is the usual first step taken in solving the equation $3 x^{2}-2 x=8$ by completing the square?

Question 54

To complete the square of $2 x^{2}+4 x=8$ , is it ever a good idea to divide by the coefficient of $x^{2}$ ?

Question 55

To complete the square for an equation in the form $x^{2}-a x=b$ , is it ever appropriate to subtract a positive number from each side?

Question 56

Use the equation $5 x^{2}+6 x=c$ to explain how to solve a quadratic equation by completing the square.

Question 57

Choose the one alternative that best completes the statement or answers the question.

-Which method of solving the following equation would probably be more convenient? $(5 x-4)^{2}=24$

A) Completing the square
B) Square root property

Question 58

Give a one-sentence description or explanation of the square root property.

Question 59

Find the mistake, then find the correct answer.
line $1 \quad x^{2}-6 x=-8$
line $2 \quad x^{2}-6 x+9=-8+9$
line $3 \quad(x-3)^{2}=1$
line $4 \quad x-3=\sqrt{1}$
line $5 \quad x-3=1$
line $6 \quad x-3+3=1+3$
line $7 \quad x=4$
line $8 \quad$ The solution set is $\{4\}$ .

Question 60

Find the mistake, then find the correct answer.
Solve for $\mathrm{x}: \mathrm{x}^{2}=50$
line $1 \quad \sqrt{x^{2}}=\sqrt{50}$
line $2 \quad x=2 \sqrt{5}$ or $x=-2 \sqrt{5}$
line 3 The solution set is $\{2 \sqrt{5},-2 \sqrt{5}\}$ .

Question 61

Find the mistake, then find the correct answer.
Solve for $\mathrm{x}:(\mathrm{x}-5)^{2}=-13$
line $1 \quad x-5=\sqrt{13}$
line $2 \quad x=5+\sqrt{13}$ or $x=5-\sqrt{13}$
line 3 The solution set is $\{5+\sqrt{13}, 5-\sqrt{13}\}$ .

Question 62

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $2 n^{2}=-10 n-5$

A) $\left\{\frac{-5+\sqrt{35}}{2}, \frac{-5-\sqrt{35}}{2}\right\}$

B) $\left\{\frac{-5+\sqrt{15}}{2}, \frac{-5-\sqrt{15}}{2}\right\}$

C) $\left\{\frac{-10+\sqrt{15}}{2}, \frac{-10-\sqrt{15}}{2}\right\}$

D) $\left\{\frac{-5+\sqrt{15}}{4}, \frac{-5-\sqrt{15}}{4}\right\}$

Question 63

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $\frac{z^{2}}{3}=\frac{z}{2}+\frac{5}{6}$

A) $\left\{-1, \frac{5}{2}\right\}$

B) $\left\{\frac{3+2 \sqrt{10}}{4}, \frac{3-2 \sqrt{10}}{4}\right\}$

C) $\left\{\frac{5}{2}\right\}$

D) $\{-1\}$

Question 64

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $\frac{3}{4} s^{2}+\frac{1}{2} s+\frac{1}{12}=0$

A) $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$

B) $\left\{-\frac{1}{3}\right\}$

C) $\left\{\frac{1}{3}\right\}$

D) $\left\{\frac{1}{3},-\frac{1}{3}\right\}$

Question 65

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $3 x(x+5)=2$

A) $\{1\}$

B) $\left\{-\frac{3}{5}\right\}$

C) $\left\{\frac{15+\sqrt{249}}{6}, \frac{15-\sqrt{249}}{6}\right\}$

D) $\left\{\frac{-15+\sqrt{249}}{6}, \frac{-15-\sqrt{249}}{6}\right\}$

Question 66

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $\mathrm{a}^{2}+14 \mathrm{a}+40=0$

A) $\{2 \sqrt{10},-2 \sqrt{10}\}$
B) $\{-20,-8\}$
C) $\{-10,-4\}$
D) $\{4,10\}$

Question 67

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $9 x^{2}+2 x-7=0$

A) $\left\{\frac{9}{7}, 1\right\}$

B) $\left\{\frac{9}{7},-1\right\}$

C) $\left\{\frac{7}{9},-1\right\}$

D) $\left\{\frac{9}{7}, 0\right\}$

Question 68

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $\mathrm{x}^{2}=9-4 \mathrm{x}$

A) $\{2+\sqrt{13}\}$

B) $\{-2+2 \sqrt{13},-2-2 \sqrt{13}\}$

C) $\{-1+\sqrt{13},-1-\sqrt{13}\}$

D) $\{-2+\sqrt{13},-2-\sqrt{13}\}$

Question 69

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)

- $(2 x-1)(x+1)=6$

A) $\left\{\frac{1+\sqrt{57}}{4}, \frac{1-\sqrt{57}}{4}\right\}$

B) $\left\{\frac{1+\sqrt{57}}{2}, \frac{1-\sqrt{57}}{2}\right\}$

C) $\left\{\frac{-1+\sqrt{57}}{4}, \frac{-1-\sqrt{57}}{4}\right\}$

D) $\left\{\frac{-1+\sqrt{37}}{2}, \frac{-1-\sqrt{37}}{2}\right\}$

Question 70

Use the quadratic formula to solve the equation.

- $x^{2}+x+6=0$

A) $\left\{\frac{1+\sqrt{23}}{2}, \frac{1-\sqrt{23}}{2}\right\}$

B) $\left\{\frac{-1+\sqrt{23}}{2}, \frac{-1-\sqrt{23}}{2}\right\}$

C) $\left\{\frac{-1+\mathrm{i} \sqrt{23}}{2}, \frac{-1-\mathrm{i} \sqrt{23}}{2}\right\}$

D) $\left\{\frac{1+\mathrm{i} \sqrt{23}}{2}, \frac{1-\mathrm{i} \sqrt{23}}{2}\right\}$

Question 71

Use the quadratic formula to solve the equation.

- $8 x^{2}+7 x=-2$

A) $\left\{\frac{7+\sqrt{15}}{16}, \frac{7-\sqrt{15}}{16}\right\}$

B) $\left\{\frac{-7+\sqrt{15}}{16}, \frac{-7-\sqrt{15}}{16}\right\}$

C) $\left\{\frac{-7+\mathrm{i} \sqrt{15}}{16}, \frac{-7-\mathrm{i} \sqrt{15}}{16}\right\}$

D) $\left\{\frac{7+\mathrm{i} \sqrt{15}}{16}, \frac{7-\mathrm{i} \sqrt{15}}{16}\right\}$

Question 72

Use the quadratic formula to solve the equation.

- $2 x^{2}=-5 x-7$

A) $\left\{\frac{-5+\sqrt{31}}{4}, \frac{-5-\sqrt{31}}{4}\right\}$

B) $\left\{\frac{-5+\mathrm{i} \sqrt{31}}{4}, \frac{-5-\mathrm{i} \sqrt{31}}{4}\right\}$

C) $\left\{\frac{5+\mathrm{i} \sqrt{31}}{4}, \frac{5-\mathrm{i} \sqrt{31}}{4}\right\}$

D) $\left\{\frac{5+\sqrt{31}}{4}, \frac{5-\sqrt{31}}{4}\right\}$

Question 73

Use the quadratic formula to solve the equation.

- $8 x^{2}-3 x+8=0$

A) $\left\{\frac{3+\sqrt{247}}{16}, \frac{3-\sqrt{247}}{16}\right\}$

B) $\left\{\frac{-3+\mathrm{i} \sqrt{247}}{16}, \frac{-3-\mathrm{i} \sqrt{247}}{16}\right\}$

C) $\left\{\frac{-3+\sqrt{247}}{16}, \frac{-3-\sqrt{247}}{16}\right\}$

D) $\left\{\frac{3+\mathrm{i} \sqrt{247}}{16}, \frac{3-\mathrm{i} \sqrt{247}}{16}\right\}$

Question 74

Use the quadratic formula to solve the equation.

- $x^{2}-\frac{1}{5} x=-\frac{7}{10}$

A) $\left\{\frac{-1+\mathrm{i} \sqrt{69}}{10}, \frac{-1-\mathrm{i} \sqrt{69}}{10}\right\}$

B) $\left\{0,-\frac{7}{2} \mathrm{i}\right\}$

C) $\left\{\frac{1+\mathrm{i} \sqrt{69}}{10}, \frac{1-\mathrm{i} \sqrt{69}}{10}\right\}$

D) $\left\{\frac{1}{5} \mathrm{i}, 0\right\}$

Question 75

Use the quadratic formula to solve the equation.

- $7 x^{2}+3 x+6=0$

A) $\left\{\frac{-3+i \sqrt{159}}{14}, \frac{-3-i \sqrt{159}}{14}\right\}$

B) $\left\{\frac{3+\mathrm{i} \sqrt{159}}{14}, \frac{3-\mathrm{i} \sqrt{159}}{14}\right\}$

C) $\left\{\frac{-3+\mathrm{i} \sqrt{159}}{7}, \frac{-3-\mathrm{i} \sqrt{159}}{7}\right\}$

D) $\left\{\frac{3+\mathrm{i} \sqrt{159}}{7}, \frac{3-\mathrm{i} \sqrt{159}}{7}\right\}$

Question 76

Use the quadratic formula to solve the equation.

- $0.7 x^{2}+0.3 x+0.5=0$

A) $\left\{\frac{3+\mathrm{i} \sqrt{131}}{14}, \frac{3-\mathrm{i} \sqrt{131}}{14}\right\}$

B) $\left\{\frac{3+\mathrm{i} \sqrt{131}}{7}, \frac{3-\mathrm{i} \sqrt{131}}{7}\right\}$

C) $\left\{\frac{-3+\mathrm{i} \sqrt{131}}{14}, \frac{-3-\mathrm{i} \sqrt{131}}{14}\right\}$

D) $\left\{\frac{-3+\mathrm{i} \sqrt{131}}{7}, \frac{-3-\mathrm{i} \sqrt{131}}{7}\right\}$

Question 77

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.

- $s^{2}-7 s+6=0$

A) Two rational solutions
B) One rational solution
C) Two irrational solutions
D) Two nonreal complex solutions

Question 78

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.

- $\mathrm{t}^{2}-8 \mathrm{t}+16=0$

A) One rational solution
B) Two rational solutions
C) Two nonreal complex solutions
D) Two irrational solutions

Question 79

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.

- $\mathrm{v}^{2}-5 \mathrm{v}-2=0$

A) One rational solution
B) Two nonreal complex solutions
C) Two irrational solutions
D) Two rational solutions

Question 80

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.

- $w^{2}+3 w+5=0$

A) Two nonreal complex solutions
B) Two rational solutions
C) One rational solution
D) Two irrational solutions