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Question

Let p(x)=x25x+a and q(x)=x23x+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.


A

4

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B

5

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C

6

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D

7

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Solution

The correct option is D

7


HCF=x1

p(x)=x25x+a

=x25x+4

=(x1)(x4) .......... (1)

and q(x)=x23x+b=x23x+2

=(x1)(x2) ..........(2)

k(x)=(x1)(x2)(x4)

Hence (x1)+k(x)=(x1)+(x1)(x2)(x4)

=(x1)(x3)2

Hence sum of roots = 7


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