Question

For the polynomial 3x^3+4x^2-7x+2=0, are there any other rational roots other than 2/3? When I try to factor 3x^2+6x-3, I get nowhere.

Answer 1

\[
\frac23\ |\ 3\ 4\ -7\ \ \ \ \ 2\\
\ \ \ \ \ \ \ \ \ 2\ \ \ \ \ 4\ -2\\
\ \ \ \ \ \ 3\ 6\ -3\ \ \ \ \ 0
\\
(x-\frac23)(3x^2+6x-3)=(3x-2)(x^2+2x-1)=0\\
x^2+2x-1=0\\
x=\frac{-2\pm2\sqrt2}2=-1\pm\sqrt2
\]

Answer 2

So, no, there are no more rational roots... the other 2 are irrational.

Answer 3

Okay. Thanks