2017 · Q20
If the HCF of polynomials f(x)=(x-2)(x²+3x+a) and g(x)=(x+2)(x²+2x+b) is (x²+x-2), then what are the values of a and b respectively ?
Elementary MathematicsHCF and LCM
- A2,2
- B2,-3
- C-1,-3
- D-2,-1
Explanation
x²+x−2 = (x−1)(x+2). For f(x) = (x−2)(x²+3x+a) to contain (x+2), we need (−2)²+3(−2)+a = 0, i.e. a = 2. For g(x) = (x+2)(x²+2x+b) to contain (x−1), we need 1²+2+b = 0, i.e. b = −3. Checking: f = (x−2)(x+1)(x+2) and g = (x+2)(x+3)(x−1), whose HCF is indeed (x+2)(x−1) = x²+x−2. Hence option (B) 2,−3.