# Finding Zeros in a Polynomial

Printable View

• Apr 8th 2008, 09:03 AM
badandy328
Finding Zeros in a Polynomial
Hey guys. I'm having trouble with this problem.

Find all of the zeros of the following polynomial and give them in a comma-separated list. If there are no zeros, enter None .
http://hosted.webwork.rochester.edu/...552d56dbe1.png
Note: complex numbers should be in the form (a+bi).
• Apr 8th 2008, 09:36 AM
topher0805
First thing you should not is that when x=1, the function is equal to 0.

Using long division, you can find that:

$x^4+4x^3-3x^2+8x-10 = (x-1)(x^3+5x^2+2x+10)$

Note that when $x=-5$ , $(x^3+5x^2+2x+10)=0$

Using long division, you can find that:

$(x^3+5x^2+2x+10) = (x+5)(x^2+2)$

So we have that:

$x^4+4x^3-3x^2+8x-10 = (x-1)(x+5)(x^2+2)$

Now just find the values of x that make this expression equal to 0.
• Apr 8th 2008, 05:18 PM
badandy328
ok, I see how the zeros are 1,-5,+2i and -2i. But how do I write 2i in a+bi form?
• Apr 8th 2008, 05:24 PM
Mathstud28
Haha
Quote:

Originally Posted by badandy328
ok, I see how the zeros are 1,-5,+2i and -2i. But how do I write 2i in a+bi form?

2i in $a+bi$ form is $0+2i$