p(x)=x2−5x+a, q(x)=x2−3x+b { where, a, b ∈ N} hcf(p(x),q(x))=x−1 so x – 1 is root of both p(x) & q(x) p(1)=1−5+a=0⇒a=4 q(1)=1−3+b=0⇒b=2 p(x)=x2−5x+4=(x−1)(x−4) q(x)=x2−3x+2=(x−1)(x−2) k(x)=lcm(p(x),q(x))=(x−1)(x−2)(x−4) (x−1)+k(x)=(x−1)+(x−1)(x−2)(x−4) =(x−1)[1+x2−6x+8] =(x−1)(x2−6x+9) =(x−1)(x−3)2 roots 1, 3, 3 Sum of roots = 1 + 3 + 3 = 7