1. Equations & Inequalities

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$-3,2$

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$4,5$

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$8x^2-72=0$

For each equation, (b) solve for y in terms of x. See Example 8.

$2x^2+4xy-3y^2=2$

For each equation, (b) solve for y in terms of x. See Example 8.

$4x^2-2xy+3y^2=2$

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$h=-16t^2+v_{0}t+s_0$, for t

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$r=r_0+\left(\frac{1}{2}\right)a{t}^2$, for t

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. $s=\left(\frac{1}{2}\right)g{t}^2$, for t

Solve each cubic equation using factoring and the quadratic formula. See Example 7.

$x^3+64=0$

Solve each cubic equation using factoring and the quadratic formula. See Example 7.

$x^3-27=0$

Solve each equation using the quadratic formula. See Examples 5 and 6.

$(4x-1)(x+2)=4x$