# Zeros of polynomials

• Oct 22nd 2008, 10:16 AM
aquavit
Zeros of polynomials
For some reason this is throwing me off.

Given :http://www.reynoldszoo.com/1/given.jpg

Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?
http://www.reynoldszoo.com/1/ans.jpg

And how do I get the complex zeros?

Sorry for having to use pics but i cant figure out the way you all do it yet :)
• Oct 22nd 2008, 10:22 AM
earboth
Quote:

Originally Posted by aquavit
For some reason this is throwing me off.

Given :http://www.reynoldszoo.com/1/given.jpg

Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?
http://www.reynoldszoo.com/1/ans.jpg

And how do I get the complex zeros?

Sorry for having to use pics but i cant figure out the way you all do it yet :)

1. Have a look here: http://www.mathhelpforum.com/math-he...-tutorial.html

2. Actually there are 4 zeros if you count the -1 twice. The graph of the function touches the x-axis at x = -1. (In Germany such a case is considered to be a double-zero)
• Oct 22nd 2008, 10:23 AM
masters
Quote:

Originally Posted by aquavit
For some reason this is throwing me off.

Given :http://www.reynoldszoo.com/1/given.jpg

Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?
http://www.reynoldszoo.com/1/ans.jpg

And how do I get the complex zeros?

Sorry for having to use pics but i cant figure out the way you all do it yet :)

Using the rational roots theorem you discover that -1 is a root twice.

Using synthetic division, you can factor the original polynomial down to:

\$\displaystyle f(x)=(x-1)(x-1)(x^2-4x+8)\$