1. Equations & Inequalities

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.x^2 - 4x - 5 = 0

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.2x^2 - 11x + 3 = 0

For each equation, (b) solve for y in terms of x. See Example 8. 2x^2 + 4xy - 3y^2 = 2

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. 3x^2 + 5x + 2 = 0

Solve each equation in Exercises 83–108 by the method of your choice.5x^2 + 2 = 11x

Solve each equation in Exercises 83–108 by the method of your choice.3x^2 = 60

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) 4, 5

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) -3, 2

Solve each equation in Exercises 83–108 by the method of your choice.9 - 6x + x^2 = 0

Solve each equation in Exercises 83–108 by the method of your choice.4x^2 - 16 = 0

Solve each equation in Exercises 83–108 by the method of your choice.x^2 - 4x + 29 = 0

Exercises 100–102 will help you prepare for the material covered in the next section.Factor: x^2 - 6x + 9

Solve each equation in Exercises 83–108 by the method of your choice.1/x + 1/(x + 3) = 1/4

Solve each equation in Exercises 83–108 by the method of your choice.2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)

Solve each equation in Exercises 83–108 by the method of your choice.3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)