(2)

Let .

Clearly, it is an even degree whose last term is negative and coefficient of highest degree term is positive. So, it has at least two real roots one positive and one negative.

We have, and

Thus, one real root lies between 0 and 1 , and other lies between -1 and 0 .
Now,

Clearly, has no real root and being an odd degree polynomial, has at least one real root. So, by the algebraic interpretation of Rolle's theorem has exactly one real root. Consequently, has exactly two real roots.

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