Explain why :
P(x) = x^50 - 5x^25 + x^2 - 1
has no rational zeros. Use theory!
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