Solving Quadratic Equations. Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = -4 -7 3 3 -7x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)

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Presentation transcript:

Solving Quadratic Equations

Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)

Standard Form ax² + bx + c To solve for x, we set the equation equal to zero. ax² + bx + c = 0 Or, from our previous example; x² - 4x – 21 = 0. We then set out factored form equal to zero: (x + 3)(x – 7) = 0

Zero-Product Property If ab = 0, then a = 0 or b = 0. Example: If (x + 3)(x – 7) = 0, then (x + 3) = 0 or (x – 7) = 0. (x + 3)(x – 7) = 0 x + 3 = 0 x – 7 = 0 x = -3 x = 7

Solve by factoring. x² + 7x = 18  x² + 7x – 18 = 0 x² -18 a*c = -18 b = 7 x + = -18 = x 9x9x x 9 (GCF) x-2 (x – 2)(x + 9) = 0 x – 2 = 0 x + 9 = 0 x = 2 x = -9

Solve by factoring. 2x² + 4x = 6

Solve by factoring. 16x² = 8x 16x² - 8x = 0 8x(2x – 1) = 08x = 0 2x – 1 = 0 x = 0 x = 1 2