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.) See Example 9.

$9x^2+11x+4=0$

Solve each equation in Exercises 83–108 by the method of your choice. $x^2-2x=1$

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x² - 20)/(x² - 7x + 12)

Find all values of x satisfying the given conditions. y₁ = 2x/(x + 2), y₂ = 3/(x + 4), and y₁ + y₂ = 1

List all numbers that must be excluded from the domain of each rational expression. 3/(2x² + 4x - 9)

Solve each equation by the method of your choice. √2 x² + 3x - 2√2 = 0

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. $\mid 2x^2-4\mid =\mid 2x^2\mid$

Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

Solve each equation. See Example 7. (x²+24)^1/4 = 3

Solve each equation. See Example 7. (x-3)^2/5 = 4

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x² - 2x + 2