Question

If f(x)=x²5x+a and g(x)=x²+3x+b have a common factor then find the common factor.

Answer 1

Let the common factor be x – k, we have f(k) = g(k) = 0 k2 + 5k + p = k2 + 3k + q

k = (q - p)/2 Substituting ‘k’ in x2 + 5x + p = 0, we get [(q - p)/2]2 + 5[(q - p)/2] + p = 0 (p - q)2 = 2(3p - 5q)