Let f x be a quadratic polynomial such that f - 2 + f 3 = 0 . If one of the roots of f x = 0 is - 1 , then the sum of the roots of f x = 0 is equal to

Step-by-step solution

Let f x = a x 2 + b x + c Given, f - 2 + f 3 = 0 ⇒ 4 a - 2 b + c + 9 a + 3 b + c = 0 ⇒    13 a + b + 2 c = 0               . . . i Since - 1 is a root of f x = 0 . So, f - 1 = 0 ⇒ a - b + c = 0             . . . ii On solving equations i & ii , we get 11 a + 3 b = 0 ⇒ - b a = 11 3 Now, we know that sum of the roots of a x 2 + b x + c = 0 is - b a . ∴ The sum of the roots of f x = 0 is 11 3 .