Let $p (x) = x^{2} - 5 x + a$ and $q (x) = x^{2} - 3 x + b$ , where a and b are positive integers.Suppose hcf $(p (x), q (x) = x - 1$ and $k (x) = l c m$ $(p (x), q (x))$ .If the coefficient of the highest degree term of k (x) is 1,the sum of the roots of $(x - 1) + k (x)$ is

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Solution

The correct option is D 7
$∴ H C F = x - 1$
$\Rightarrow p (x) = x^{2} - 5 x + a$
$x^{2} - 5 x + 4$ ........................(1)
$(x - 1) (x - 2)$
and $q (x) x^{2} - 3 x + b = X^{2} - 3 x + 2$
= $(x - 1) (x - 2)$ ......................(2)
$\Rightarrow k (x) = (x - 1) (x - 2) (x - 4)$
Hence
$(x - 1) + R (x) = (x - 1) + (x - 1) (x - 2) (x - 2) (x - 4) = (x - 1) (x - 3)^{2}$
Hence sum of roots =7

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Let $p (x) = x^{2} - 5 x + a$ and $q (x) = x^{2} - 3 x + b$ , where a and b are positive integers. Suppose hof(p(x),q(x)) = x – 1 and k(x) = 1cm (p(x), q(x)). If the coefficient of the highest degree term of k(x) is 1, the sum of the roots of (x – 1) + k(x) is.