If the G.C.D. of the polynomials $x^{3} - 3 x^{2} + p x + 24$ and $x^{2} - 7 x + q$ is $(x - 2)$ , then the value of $(p + q)$ is

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Solution

The correct option is C $0$
$(x - 2)$ is GCD of 2 Polynomials $\Rightarrow x = 2$ is
root of 2 Poly.
$\Rightarrow 2^{2} - 7 \times 2 + q = 0 \Rightarrow q = 10$
$2^{3} - {3.2}^{2} + 2 p + 24 = 0 \Rightarrow p = - 10$
$∴ p + q = 0$

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