Question

Let $p\left(x\right)=x^2–5x+a$ and $q\left(x\right)=x^2–3x+b$, 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. 5
• B. 4
• C. 7
• D. 6

Answer 1

The correct option is C

7

$\therefore HCF=x-1$

$\Rightarrow p\left(x\right)=x^2-5x+a$

$=x^2-5x+4$

$=(x-1)(x-4)$ .......... (1)

and $q\left(x\right)=x^2-3x+b=x^2-3x+2$

$=(x-1)(x-2)$ ..........(2)

$\Rightarrow k\left(x\right)=(x-1)(x-2)(x-4)$

Hence $(x-1)+k\left(x\right)=(x-1)+(x-1)(x-2)(x-4)$

$=(x-1)(x-3{)}^2$

Hence sum of roots = $7$