Question

If 2a + 3b + 6c = 0 (a, b, c ∈ R) then the quadratic equation ax² + bx + c = 0 has
(a) At least one in (0, 1)
(b) At least one root in [2, 3]
(c) At least one root in [4, 5]
(d) none of these

Answer 1

As f(0) = f(1) = 0 and f(x) is continuous and differentiable also in [0, 1].
Therefore, By Rolle’s theorem f ' (x) = 0
=> ax² + bx + c = 0 has at least one root in the interval (0, 1).