Solution:
Consider the function
We find that and,
Therefore, 0 and 1 are roots of the polynomial
Consequently, there exists at least one root of the polynomial
lying between 0 and 1.
If the at least one root of the equation lies in the interval
Consider the function
We find that and,
Therefore, 0 and 1 are roots of the polynomial
Consequently, there exists at least one root of the polynomial
lying between 0 and 1.