# Polynomial Function

• Sep 27th 2008, 04:36 AM
magentarita
Polynomial Function
For the polynomial function below, state the zeros and the multiplicity.

f(x) = (x + sqrt{3})^2 (x - 2)^4

What is the easiest way or method for finding the zeros of polynomial functions?
• Sep 27th 2008, 04:37 AM
Moo
Quote:

Originally Posted by magentarita
For the polynomial function below, state the zeros and the multiplicity.

f(x) = (x + sqrt{3})^2 (x - 2)^4

What is the easiest way or method for finding the zeros of polynomial functions?

To see its factorised form, like what you have.

Don't you have any textbook or teacher's notes ? (Thinking)

You can look here too : Polynomial Graphs: Zeroes and Their Multiplicities (which I found by googling "polynomial multiplicity" :rolleyes: )
• Sep 27th 2008, 09:38 PM
magentarita
yes
Quote:

Originally Posted by Moo
To see its factorised form, like what you have.

Don't you have any textbook or teacher's notes ? (Thinking)

You can look here too : Polynomial Graphs: Zeroes and Their Multiplicities (which I found by googling "polynomial multiplicity" :rolleyes: )

Yes, I have the textbook and teacher's notes but if I understood that there would be no reason to post questions here.
• Sep 28th 2008, 11:23 AM
mikedwd
the root negetive root three has a multiplicity of 2
the root two has a multiplicity of 4

if you set each factor equal to zero and solve for x, that gives you the root from factored form

the exponent that the factor is raised to is the multiplicity, because that is the number of times that that factor is a factor of the polynomial (maybe it's easier to understand if i show you an example:

x(squared)-4x+4
factors to (x-2)(x-2)
which is the same as (x-2)squared

the root is x-2=0 so x=2
so the root x=2 has a multiplicity of 2 in my example)

in your situation there is a root (x-2) raised to the 4th, so the root x=2 has a multiplicity of 4
• Sep 28th 2008, 09:32 PM
magentarita
good..
Quote:

Originally Posted by mikedwd
the root negetive root three has a multiplicity of 2
the root two has a multiplicity of 4

if you set each factor equal to zero and solve for x, that gives you the root from factored form

the exponent that the factor is raised to is the multiplicity, because that is the number of times that that factor is a factor of the polynomial (maybe it's easier to understand if i show you an example:

x(squared)-4x+4
factors to (x-2)(x-2)
which is the same as (x-2)squared

the root is x-2=0 so x=2
so the root x=2 has a multiplicity of 2 in my example)

in your situation there is a root (x-2) raised to the 4th, so the root x=2 has a multiplicity of 4