Question

If 2a + 3b + 6c = 0, then prove that at least one root of the equation ax² + bx + c = 0 lies in the interval (0, 1).

Answer 1

 Let f (x) = ax² + bx + c.

Therefore,

Since f (0) = f(1) = 0, hence, there exists at least one point c in between 0 and 1, such that f '(c) = 0, by Rolle’s theorem.