Explain why :

P(x) = x^50 - 5x^25 + x^2 - 1

has no rational zeros. Use theory!

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- Dec 16th 2008, 11:57 AMneedhelp75Anybody here good with theory?
Explain why :

P(x) = x^50 - 5x^25 + x^2 - 1

has no rational zeros. Use theory! - Dec 16th 2008, 12:12 PMCaptainBlack
The rational root theorem tell us that is this has a rational root it is of the form a/b where a is a divisor of the constant term and b a divisor of the coefficient of the highest power of the variable. So in this case all the rational roots (of any) are +1 or -1.

Check if these are roots, if not this has no rational roots.

CB - Dec 16th 2008, 12:16 PMgalactus
Look into the Rational Root theorem. The possible candidates for real roots are 1 and -1 (why?)

Does 1 or -1 satisfy the equation $\displaystyle x^{50}-5x^{25}+x^{2}-1=0$?. - Dec 16th 2008, 07:09 PMneedhelp75many thanks
(Bow)