Exam 14: Quadratic Equations

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

Plot $y=x^{2}+x-12$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

Plot $y=6 x^{2}-5 x-6$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

For a chemical reaction $\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}$ , the equilibrium concentration of $\mathrm{NO}$ is given by $2 x$ , where $\frac{x^{2}}{(0.100-x)(0.100-x)}=0.100$ . Determine the equilibrium concentration of NO.

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}+14 x-27=0$

Plot $y=-2 x^{2}+4 x+1$ . 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: $x(3 x-4)=4(x+4)+1$

Solve for $x$ by completing the square: $x^{2}-8 x+15=0$

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

Solve for all real values of $x: 12 x^{-2}=8-29 x^{-1}$

Use the quadratic formula to solve for $x$ to three significant digits: $3 x^{2}+4 x+2=0$

Solve for all real values of $x: x^{6}+2 x^{3}=-1$

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

A rectangle is $3 \mathrm{~m}$ longer than twice its width and has an area of $324 \mathrm{~m}^{2}$ . What are its dimensions?

Plot $y=-4 x^{2}+2 x+3$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

Solve for $x$ by factoring: $2 x(x+1)-30=30$

Solve for $x$ in terms of $a: 35 x^{2}-17 a x+2 a^{2}=0$

One root of $3 x^{3}-5 x^{2}-16 x+12=0$ is $x=3$ . Find the remaining roots.

Find a number which added to its square equals 56.

Solve for all values of $x: x^{5}-1025 x^{5 / 2}+1024=0$