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 ?

thanks.

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- Dec 9th 2010, 12:10 AMZOOZprove the Square root
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 ?

thanks. - Dec 9th 2010, 01:33 AMHallsofIvy
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. - Dec 9th 2010, 01:48 AMBAdhi
functions are not printed well sir,

- Dec 9th 2010, 04:23 AMZOOZ
well yes i mean than 2 root.

but i not Understand what you Write: "If you take that to be f', then [tex]f(x)= \frac{1}{5}x^5- \frac{1}{2}x^4+ 2x^3+ \frac{m}{2}x^2+ mx+ C[tex]: what is mean?

did you mean f'=4x^3+6x^2+12x+m?

thanks - Dec 9th 2010, 04:24 AMZOOZ
how did you get it ?