mac1147_lecture5_1_b

# mac1147_lecture5_1_b - L5 Quadratic Equations and the...

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50 L5 Quadratic Equations and the Quadratic Formula; Applications; Complex Numbers Quadratic Equations A quadratic equation is an equation of the form 2 0 ax bx c + += where a, b, and c are real numbers and 0 a . Solving by Factoring Zero-Product Property : If 0 ab = , then Example : Solve by factoring. 2 10 9 x x −= 2 41 2 9 0 x x −+ =

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51 The Square Roots Method : The solution set to 2 x p = (0 ) p is the set of all square roots of the number p , that is x p Example . Solve using the Square Roots Method. 2 25 x = 2 (2 )3 x += Solving Quadratic Equations by Completing the Square : 2 0, 0 ax bx c a + 1. Make sure that 1 a = ; if not, divide each term by a . 2. Get the constant on the right-hand side of the equation. 3. Take 1/2 of the coefficient of x , square it, and add this number to both sides of the equation. 4. Factor the left-hand side into a perfect square. 5. Solve for x using the Square Roots Method.
52 Example : Solve by completing the square. 2 83 0 x x −+ =

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53 The Quadratic Formula The quadratic equation 2 00 ax bx c a + += has the solutions 2 4 2 bb a c x a −± = The quantity 2 4 ba c , denoted D , is called the discriminant .
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## This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture5_1_b - L5 Quadratic Equations and the...

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