# Finding Zeros of a Polynomial

• Feb 21st 2010, 03:56 PM
JennyFlowers
Finding Zeros of a Polynomial
Hello, all.

I need to find the zeros of the following polynomial so that I can graph it:

\$\displaystyle f(x)=3x^2-x^4-2x\$

First I factored out x and got:

\$\displaystyle x(-x^3+3x-2)\$

I used synthetic division to find another zero (-2) and so I now have:

\$\displaystyle x(x+2)(-x^2+2x-1)\$

I'm not sure how I can go any further. Can \$\displaystyle -x^2+2x-1\$ be factored out?

Thanks!
• Feb 21st 2010, 04:19 PM
skeeter
Quote:

Originally Posted by JennyFlowers
Hello, all.

I need to find the zeros of the following polynomial so that I can graph it:

\$\displaystyle f(x)=3x^2-x^4-2x\$

First I factored out x and got:

\$\displaystyle x(-x^3+3x-2)\$

I used synthetic division to find another zero (-2) and so I now have:

\$\displaystyle x(x+2)(-x^2+2x-1)\$

I'm not sure how I can go any further. Can \$\displaystyle -x^2+2x-1\$ be factored out?

Thanks!

\$\displaystyle -(x^2-2x+1) = -(x-1)^2\$