Any help today would be appreciated, thanks.

[link2110]

Homework Statement

wtihout using a graphing calc, find the rational roots of P(x) = 2x^4-5x^3+5x^2-5x+3

Homework Equations

The Attempt at a Solution

The answers are 1 and 3/2, because this is a homework question. I don't know how they got that though. If anybody can help me today that would be appreciated.

Thanks,
~Link2110

 

[gabbagabbahey]

Hint: Look up the "rational root theorem"

 

[Dick]

Check the wikipedia entry on the "rational roots theorem". http://en.wikipedia.org/wiki/Rational_root_theorem It's pretty clear.

 

[HallsofIvy]

If that isn't clear (thanks, Dick) the rational root theorem says that any rational root of $a_ix^i+ a_{i-1}x^{i-1}+ \cdot\cdot\cdot+ a_1x+ a_0$ must be of the form m/n where m divided $a_i$ and n divides $a_0$ (that's because if x= m/n is root then (x- m/n)= (1/n)(nx- m) must be a factor). Here, $a_n= a_4= 2$ and $a_0= 3$. Since those are prime, there are not a whole lot of possiblities.