Lesson 10.4: Solving Quadratic Equations Using the Quadratic Formula, pg. 546

Goals:To solve quadratic equations by using the Quadratic Formula.To use the discriminant to determine the number and type of roots of a quadratic equation.

Quadratic Formula

The solutions of a quadratic equation of the form ax² + bx + c = 0, where a ≠ 0, are given by the following formula.

To solve quadratic equations using the quadratic formula, the equation must be set equal to ZERO

a

b

2

4ac- b2

Example 1: Solve by using the quadratic formula.

1. x² - 2x – 35 = 0

Round to the nearest tenth if necessary.

2. 15x² - 8x = 4

3. 2(12g² - g) = 15

4. 3x² + 5x +11

Discriminant:To find the number and types of roots of a quadratic equation use b² - 4ac

b² - 4ac > 0; 2 real roots

positive

b² - 4ac = 0; 1 real root

b² - 4ac < 0; no real roots

negative

a

b

2

4ac- b2x =

antdiscrimin

Ex. 2: Describe the roots using the discriminant.

1. 4x² - 2x + 14 = 0 2. x² + 24x = -144

3. 3x² + 10x = 12 4. x² - 11x + 10 = 0