i need to use with Rolle's theorem to prove that this Polynomial has no then 2 Square root, Regardless of the values m and n.
i not find any Square root is can be?
someone can show me the correct way to Solve it ?
This problem, as stated, does not require you to find any roots, just determine that roots exist. (And not "square roots". Square roots are specifically roots to the equation .) It's not clear to me what you mean by "no then 2 roots". What does the "then" mean? Do you mean that, for all m and n, it has either 0 or 2 roots, but never 1, 3, or 4?
Rolle's theorem says that if f(a)= f(b)= 0 then there exist some number, c, between a and b, such that f'(c)= 0. You want to show that . If you take that to be f', then for some number C. You can always choose C to make f= 0 for a given x.