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 :

Solution

Maths sir · 4 steps

You know one root is 3, so write f(x) = a(x-3)(x-α) and let the condition find α.

1. Factor form. Since 3 is a root, take f(x) = a(x-3)(x-α) with a ≠ 0, where α is the other root.
2. Evaluate both values. f(-1) = a(-4)(-1-α) = 4a(1+α). Next, f(2) = a(-1)(2-α) = a(α-2).

   f(-1) + f(2) = a(4 + 4α + α - 2) = a(5α + 2) = 0

3. Solve. Because a ≠ 0, we get 5α + 2 = 0, so α = -2/5 = -0.4.
4. So. The other root is -0.4, which lies in (-1, 0). The answer is (c).

The idea to keep. When one root is given, write the quadratic as a(x-r)(x-α). Any condition on its values becomes a linear equation in α, and a cancels.

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