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 :

Solution

Maths sir · 3 steps

You already know one root, so write f(x) in factor form and let the given condition find the other root.

1. Factor form. Since -1 is a root, write f(x) = a(x+1)(x-β) with a ≠ 0, where β is the unknown second root.
2. Evaluate both values. f(-2) = a(-1)(-2-β) = a(2+β) and f(3) = a(4)(3-β) = a(12-4β).

   a(2+β) + a(12-4β) = 0 ⇒ 14 - 3β = 0 ⇒ β = 14/3

3. So. The sum of the roots is -1 + 14/3 = 11/3, which is option (a).

The idea to keep. When a root is given, start from a(x-α)(x-β). The leading coefficient a cancels out of any condition like f(p)+f(q)=0, leaving one equation in the unknown root.

Answer from the NTA final answer key. Solution by PrepWiser.