To determine To solve: The equation 3 x − 2 − 7 x − 1 − 6 = 0 algebraically. Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x 2 + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation 3 x − 2 − 7 x − 1 − 6 = 0 . In order to find the value of x , first rewrite the equation in quadratic form. Substitute y = x − 1 in 3 x − 2 − 7 x − 1 − 6 = 0 and simplify the equation as follows. 3 y 2 − 7 y − 6 = 0 3 y 2 − 9 y + 2 y − 6 = 0 3 y ( y − 3 ) + 2 ( y − 3 ) = 0 ( 3 y + 2 ) ( y − 3 ) = 0 On further simplification, 3 y + 2 = 0 or y − 3 = 0 3 y = − 2 or y = 3 x − 1 = − 2 3 or x − 1 = 3 [ ∵ y = x − 1 ] x = − 3 2 or x = 1 3 Thus, the solutions of the equation are x = − 3 2 , and x = 1 3 _

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 14.3, Problem 5E

To determine

To solve: The equation 3x−2−7x−1−6=0 algebraically.

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Chapter 14.3, Problem 4E

Chapter 14.3, Problem 6E

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