1. Equations & Inequalities

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.) 3x² + 5x + 2 = 0

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

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

For each equation, solve for x in terms of y. 2x² + 4xy - 3y² = 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.

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

Solve each equation using the quadratic formula. (2/3)x² + (1/4)x = 3

Solve each equation using the quadratic formula. -4x² = -12x + 11

Solve each equation using the quadratic formula. x² = 2x - 5

Solve each equation. (2x+1)(x-4) = x

Height of a Projectile A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t²+v₀t. In each exercise, find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v₀. Round answers to the nearest hundredth if necessary. v₀=32