Question

The quadratic equation 3a^2+2bx+c=0 has at least one root between 0 and 1 if

Answer 1

Hey Friend....☺

Here is your answer

Lets take f(x)=ax3 + bx2 + cx + d

so, f' (x) = 3ax2 + 2bx + c

Uding Rolles theorem, (Rolle's Theorem) Let f(x) be continuous on [a, b], and differentiable on (a, b), and suppose that f (a) = f (b). Then there is some c with a < c < b such that f'(c) = 0

here (a , b) = (0 ,1)

f(0)= d and f(1) =a+b+c+d ; f(0) = f(1) which means a+b+c=0 which is true from given condition

hence there exists some c in btn (0, 1) where f '(c) =0

Hoping it helps

Thanks ....