Exam 14: Quadratic Equations

Solve for all real values of $x$ to three significant digits: $2 x^{-1}=8 x-9$

Solve for $x$ by factoring: $3 x^{2}+x-4=0$

One root of $2 x^{3}-x^{2}-4 x+3=0$ is $x=-1.5$ . Find the remaining roots.

Solve for all values of $x: x^{3 / 2}-72 x^{3 / 4}+512=0$

Solve for $x$ and $y: \frac{x^{2}}{y}+\frac{y^{2}}{x}=18$ $x+y=12$

One root of $x^{4}+2 x^{3}-2 x-1=0$ is $x=-1$ . Find the remaining roots.

Solve for $x$ and $y: x^{2}-x y+y^{2}=43$ $x-y=1$

The perimeter of a rectangle is $46 \mathrm{~cm}$ and its area is $120 \mathrm{~cm}^{2}$ . Determine the dimensions.

Solve for $x$ and $y: y+x^{2}=4$ $\frac{y}{3}=x^{2}$

Determine if the roots of $8 x^{2}+2 x-12=0$ are real or nonreal, and whether they are equal or unequal.

Solve for all real values of $x$ to three significant digits: $4 x^{6}-4 x^{3}+1=0$

Solve for $x$ and $y: 3 x^{2}+3 y^{2}=6$ $x+y=2$

For a simply supported beam of length / having a distributed load of $w \mathrm{~N} / \mathrm{m}$ , the bending moment $M$ at any distance $x$ from one end is given by the equation $M=0.5 w l x-0.5 w x^{2}$ . A $4.5 \mathrm{~m}$ beam carries a distributed load of $3.2 \mathrm{kN} / \mathrm{m}$ . At what distance from an end will the bending moment be $1.6 \mathrm{kN}$ ?

Solve for $x$ by factoring: $3 x(x-3)+22=2 x^{2}+4(x-5)$

Two airplanes start a 1000-mile journey. One plane flies $50 \mathrm{mi} . / \mathrm{h}$ faster than the other plane and arrives an hour before it. What is the speed of each plane?

Solve for all real values of $x: 6 x^{4}-x^{2}+15=0$

Disregarding units, the area of a certain equilateral triangle is equal to the perimeter. What are the side lengths of the triangle to three significant digits?

Solve this radical equation for $x$ and check: $\sqrt{x-3}=\frac{-10}{\sqrt{4-x}}$

One root of $4 x^{4}-8 x^{3}-13 x^{2}+2 x+3=0$ is $x=-1$ . Find the remaining roots.

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