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CHAPTER_ppt_11_2

# CHAPTER_ppt_11_2 - Â 11.2 Solving Quadratic Equations by...

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Unformatted text preview: Â§ 11.2 Solving Quadratic Equations by Using the Quadratic Formula Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 The Quadratic Formula Another technique for solving quadratic equations is to use the quadratic formula . The formula is derived from completing the square of a general quadratic equation. Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Quadratic Formula A quadratic equation written in the form, ax 2 + bx + c = 0, has the solutions a ac b b x 2 4 2- Â±- = The Quadratic Formula Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Solve 11 n 2 â€“ 9 n = 1 by the quadratic formula. 11 n 2 â€“ 9 n â€“ 1 = 0, so a = 11, b = -9, c = -1 2 9 ( 9) 4(11)( 1) 2(11) n Â±--- = 9 81 44 22 Â± + = 9 125 22 Â± = 9 5 5 22 Â± = The Quadratic Formula Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 2 8 (8) 4(1)( 20) 2(1) x- Â±-- = 8 64 80 2- Â± + = 8 144 2- Â± = 8 12 2- Â± = 20 4 or , 10 or 2 2 2- =- x 2 + 8 x â€“ 20 = 0 (multiply both sides by 8) a = 1, b = 8, c = -20...
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CHAPTER_ppt_11_2 - Â 11.2 Solving Quadratic Equations by...

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