If (x – a) is a factor of the polynomials x2 + px – q and x2 + rx – t, then prove that a = t−q/r−p
Solution: Let f(x) = x + px -q and g(x) = x2 + x – t Since x-a is factor of both f(x) and g(x) ⇒ f(a) = g(a) = 0 Now, here f(a) = a2 + pa – q and g(a) = a2 + ra- t ⇒ a2 + pa – q = a + ra – t (considering f(a) = g(a)] ⇒ pa – q = ra – t ⇒ ra – pa = t – q ⇒ a(r – p) = t – q a = t−q/r−p
