5-5 Quadratic Equations Hubarth Algebra II. Zero Product Property For every real number a, b, if ab = 0, then a = 0 or b = 0. EXAMPLEIf (x + 3)(x + 2)

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5-5 Quadratic Equations Hubarth Algebra II

Zero Product Property For every real number a, b, if ab = 0, then a = 0 or b = 0. EXAMPLEIf (x + 3)(x + 2) = 0, then x + 3 = 0 and x + 2 = 0 Solve (2x + 3)(x – 4) = 0 by using the Zero-Product Property. 2x + 3 = 0 or x – 4 = 0 2x = –3 x = – 3232 Ex 1 Using the Zero Product Property x = 4

Ex 2 Solving by Factoring Solve 3x 2 – 2x = 21 by factoring. 3x 2 – 2x – 21 = 0 (3x + 7)(x – 3) = 0 3x + 7 = 0orx – 3 = 0 3x = –7 x = – 7373 x = 3

x = ± 25 Solve 3x 2 – 75 = 0. 3x 2 – = x 2 = 75 x 2 = 25 x = ± 5 Ex 3 Solve by Finding Square Roots

The jumper is in free fall for approximately 6.1 seconds

Practice 5 seconds