Rational root therom

[kpx001]

What are the possible roots of f(x) = 2x^4 - x^3 + x^2 -12 ?
i got + or - 1,2,3,4,6,12 because they were all factors of 12. are there supose to be fractions? because i remember there being fractions.

find all complex roots of f(x)= x^4 - 6x^3 + 9x^2 + 6x - 10 using synthetic division to find the rational roots and then quadratic function.
i forgot completly how to do this. + or - 1,2,5,10 and then i forgot what to divide by etc

 

[morson]

Rational root theorem: For there to exist a root of a polynomial in the form \(\displaystyle \frac{p}{q}\\), where q isn't 0, then the only possible roots of these form are all the possible factors of the constant term divided by all the factors of the leading coefficient.

 

[kpx001]

what is p and q?

 

[tkhunny]

p is a factor of the constant term
q is a factor of the leading coefficient