Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Options

A. f(x) =0
B. f'(x)=0
C. f''(x)=0
D. none of these

Answer

B

Explanation

Rolle's theorem says between any two roots of a polynomial f(X) there is always a root of its derivative f(x)
Therefore between a and b There exist at least one root of the polymial equation f(X)=0