Exam 14: Quadratic Equations

The length of a rectangle exceeds the width by $7.0 \mathrm{~cm}$ . If the diagonal is $13.0 \mathrm{~cm}$ , determine the dimensions of the rectangle.

Find two numbers whose sum is 23 and the sum of whose squares is 277 .

Use the quadratic formula to solve for $x$ to three significant digits: $8 x^{2}+16 x+2=0$

Solve for $x$ by factoring: $4 x+\frac{6}{x}=25$

A machinist measures the radius and cross-sectional area of a metal rod. After machining the rod down and cutting its radius in half, and then by another 1.0 millimetre, the cross-sectional area has gone down by $15 \mathrm{~mm}^{2}$ . What was the original radius of the rod?

Solve for $x$ by factoring: $5 x(x+3)+18=2 x(x-3)$

Use the quadratic formula to solve for $x$ to three significant digits: $x\left(x^{2}+x+1\right)=x^{3}-28 x-1$

Solve for $x$ by completing the square: $3 x^{2}+5 x-2=0$

One root of $7 x^{3}-11 x^{2}+x+3=0$ is $x=1$ . Find the remaining roots.

Solve for $x$ by completing the square: $4 x^{2}+8 x+3=0$

Solve for $x$ by factoring: $x^{2}+5 x-84=0$

Solve for $x$ by factoring: $x^{2}-4 x+4=0$

Solve for $x$ in terms of $a: x^{2}-a x-6 a^{2}=0$

Use the quadratic formula to solve for $x$ to three significant digits: $115 x^{2}-105 x+2=0$

The square of a certain number less than the number itself, equals 67340 . What is the number?

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}+81 x-18=0$

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-5 x-130=0$

The difference of two numbers is 3 . The sum of their squares is 89 . What are the numbers?

Plot $y=4 x^{2}-10 x$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}-8 x=1$