If x2 – x – 6 and x2 + 3x – 18 have a common factor x – a then – InterviewSolution

InterviewSolution

1.

If x2 – x – 6 and x2 + 3x – 18 have a common factor x – a then find the value of a

Answer»

Let f(x) = x² – x – 6 and

g(x) = x² + 3x – 18

Given that (x – a) is a factor of both f(x) and g(x).

f(a) = g(a) = 0

⇒ a² – a – 6 = a² + 3a – 18

⇒ – 4a = – 18 + 6

⇒ – 4a = – 12

∴ a = 3

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