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mac1140_lecture8_1

# mac1140_lecture8_1 - L8 2.4 Quadratic Equations The...

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62 L8 §2.4 Quadratic Equations The quadratic equation is an equation that can be written in the form 2 0 ax bx c + + = where a, b, and c are real numbers and 0 a . Solving by factoring Zero-Factor Property : If 0 ab = , then 0 a = , or 0 b = , or both. This property can be applied to more than two factors. Important: Always set an equation of degree 2 or higher equal to zero before applying the Zero-Factor property . Example : Solve 2 3 18 21 x x + = .

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63 Example : Solve 3 4 x x = . Square Root Property : The solution set to 2 x k = is x k = ± . Note : If 0 k , k is the principle square root (nonnegative). If 0 k < , k i k = (imaginary number). Example . Solve each quadratic equation: a) 2 32 x = − b) 2 ( 3) 49 z =
64 Completing the Square : We can solve a quadratic equation 2 0 ( 0) ax bx c a + + = by completing the square . Steps (must be memorized) : 1. Make sure that 1 a = ; if not, divide each term by a . 2. Get the constant on the right side of the equation. 3. Take 1/2 of the coefficient of x and square it. 4. Add this number to both sides of the equation. 5. Factor the left-hand side into a perfect square. 6. Solve for

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