Let f x be a quadratic polynomial such that f – 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 , then its other root lies in

Step-by-step solution

Let f x = a x 2 + b x + c be a quadratic equation with roots α ,   β f 2 + f - 1 = 0 ⇒ 5 a + b + 2 c = 0 Also f 3 = 0 ⇒ 9 a + 3 b + c = 0 ⇒ a - 5 = b 13 = c 6 Product of roots α β = c a = - 6 5 We know α = 3 ⇒ β = - 2 5 ∈ - 1 , 0