Question

The LCM of polynomials (x^2+x-2)(x^2+x-a) and (x^2+x-b)(x^2+5x+a) is
(x-1)(x+2)^2 (x+3),then find the value of a and b.

Answer 1

Answer:

SOL : lcm of (x2+x-2)(x2+x-a) and (x2+x-b)(x2+5x+a) is (x-1)(x2+4+4x)(x+3) L.C.M (a,b) = (x-1)(x+2)2(x+3) a = (x2+x-2)(x2+x-a) = (x-1)(x+2)(x2+x-a) ∴ (x2+x-a) = (x-2)(x+3) ∴ (x2+x-a) = (x2+x-6) ⇒ -a = -6 ⇒ a = 6 b = (x2+x-b)(x2+5x+a) = (x2+x-b)(x2+5x+6) ∴ (x2+x-b) = (x-1)(x+2) = x2+x-2 ∴ b = 2