For what value of a, the G.C.D. of x^{2}-2x-2 | vedclass

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(B) Let $p(x) = x^{2}-2x-24$ and $q(x) = x^{2}-ax-6$.Since $(x-6)$ is the $G.C.D.$ of $p(x)$ and $q(x),$ it must be a factor of both polynomials.Accor

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Let $p(x) = x^{2}-2x-24$ and $q(x) = x^{2}-ax-6$.Since $(x-6)$ is the $G.C.D.$ of $p(x)$ and $q(x),$ it must be a factor of both polynomials.According to the Factor Theorem,if $(x-6)$ is a factor of $q(x),$ then $q(6) = 0$.Substituting $x = 6$ into $q(x)$:$q(6) = (6)^{2} - a(6) - 6 = 0$$36 - 6a - 6 = 0$$30 - 6a = 0$$6a = 30$$a = 5$Thus,the value of $a$ is $5$.

For what value of $a,$ the $G.C.D.$ of $x^{2}-2x-24$ and $x^{2}-ax-6$ is $(x-6)$?

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