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CHAPTER_ppt_11_3 - 11.3 Solving Equations by Using...

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§ 11.3 Solving Equations by Using Quadratic Methods
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Solving Quadratic Equations Solving a Quadratic Equation 1) If the equation is in the form ( ax + b ) 2 = c , use the square root property and solve. If not, go to Step 2. 2) Write the equation in standard form: ax 2 + bx + c = 0. 3) Try to solve the equation by the factoring method. If not possible, go to Step 4. 4) Solve the equation by the quadratic formula.
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Note that the directions on the previous slide did NOT include completing the square. Completing the square often involves more complicated computations with fractions, which can be avoided by using the quadratic formula. Solving Quadratic Equations
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Solve 12 x = 4 x 2 + 4. 0 = 4 x 2 – 12 x + 4 0 = 4( x 2 – 3 x + 1) Let a = 1, b = –3, c = 1 = - - ± = ) 1 ( 2 ) 1 )( 1 ( 4 ) 3 ( 3 2 x = - ± 2 4 9 3 2 5 3 ± Solving Quadratic Equations Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Solve the following quadratic equation. 0 2 1 8 5 2 = - + m m 0 ) 2 )( 2 5 ( = + - m m 0 2 0 2 5 = + = - m m or 2 5 2 - = = m m or 0 4 8 5 2 = - + m m (multiply both sides by 8) Solving Quadratic Equations Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 The steps we detailed in solving quadratic equations will only work if the equation is in an obviously recognizable form. Sometimes, we may have to alter the form of an equation to get it into quadratic form.
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