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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