Solution:
Consider the function
Clearly being a polynomial, is continuous on [0, 1] and differentiable on (0, 1)
Also,
and, [Given]
Thus satisfies conditions of Rolle's theorem on [0, 1]
Consequently, there exists such that i.e.
is a zero of
If Then the function has in
Consider the function
Clearly being a polynomial, is continuous on [0, 1] and differentiable on (0, 1)
Also,
and, [Given]
Thus satisfies conditions of Rolle's theorem on [0, 1]
Consequently, there exists such that i.e.
is a zero of