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If x2 - x - 6 and x2 + 3x - 18 a common factor x - a then find the value of a. |
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Answer» x2 - x - 6 and x2 + 3x - 18 \(\because\) x2 - x - 6 = 0 ⇒ x2 - 3x + 2x - 6 = 0 ⇒ x(x - 3) + 2(x - 3) = 0 ⇒ (x - 3) (x + 2) = 0 Hence, (x - 3) and (x + 2) are factors of x2 - x - 6. Now x2 + 3x - 18 = 0 ⇒ x2 + 6x - 3x - 18 = 0 ⇒ x(x + 6) - 3(x + 6) = 0 ⇒ (x + 6) (x - 3) = 0 Hence, (x - 3) and (x + 6) are factors of x2 + 3x - 18 \(\therefore\) common factor of x2 - x - 6 and x2 + 3x - 18 is x - 3 \(\therefore\) a = 3 (By comparing (x - a) with (x - 3)) |
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