Exam 14: Quadratic Equations

Solve for all real values of $x$ : $12 x^{4}+x^{2}-6=0$

Solve for $x$ by factoring: $10 x(x+1)=4(4 x+1)$

When resistors $R_{a}$ and $R_{b}$ are in series, the equivalent resistance $R=R_{a}+R_{b}$ . When resistors $R_{a}$ and $R_{b}$ are in parallel, the equivalent resistance $R$ satisfies $\frac{1}{R}=\frac{1}{R_{a}}+\frac{1}{R_{b}}$ . In the diagram below, $R_{1}=R_{2}$ and $R_{3}=100 \Omega$ . The equivalent resistance for all three resistors is $120 \Omega$ . What is the value of $R_{1}$ and $R_{2}$ ?

Solve for $x$ by completing the square: $x^{2}-3 x-9=0$

Solve for all values of $x$ : $x^{4}-13 x^{2}+36=0$

Use the quadratic formula to solve for $x$ to three significant digits: $(8 x+3)^{2}=21 x(3 x+2)+8$

Solve for $x$ by factoring: $\frac{x+2}{2}=\frac{10}{x+1}$

Solve for $x$ by factoring: $x^{2}-7 x-30=0$

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-8 x-10=0$

Write a quadratic equation that has roots $x=-1$ and $x=4 / 3$ .

One root of $3 x^{4}-10 x^{3}+10 x-3=0$ is $x=-1$ . Find the remaining roots.

Solve for $x$ by factoring: $3(x+2)^{2}=-x$

Solve for $x$ by factoring: $2 x^{2}+12 x-80=0$

Solve and check this equation. Assume $t$ is nonzero: at $-7.2 t^{2}=8 t$

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}-24 x+20=0$

A rectangle has a width that is 6 metres shorter than its length and an area of $27 \mathrm{~m}^{2}$ . Determine its dimensions.

Plot $y=2 x^{2}-2 x+3$ and label the vertex.

Solve for all real values of $x: x^{6}-19 x^{3}-216=0$

Determine if the roots of $2 x^{2}+5 x+13=0$ are real or nonreal, and whether they are equal or unequal.

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