Question

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

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}}\\ \\ \sf\:By\: Factor\: Theorem,\\ \\ \sf\: P (x) = x^2 - x - 6 \\ \\ \sf\: g (x) = x^2 + 3x - 18 \\ \\ \underline{\textsf {According to the question ; }} \\ \\ \sf\: p(a) = g(a) \\ \\ \sf\implies\:a^2 - a - 6 = a^2 + 3a - 18 \\ \\ \sf\implies\: - 4a = -12 \\ \\ \: \: \large {\boxed {\sf{a = 3}}}$