Thread: 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?

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.

See my answer to your other thread : http://www.mathhelpforum.com/math-he...tiplicity.html

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

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

Originally Posted by Moo

To see its factorised form, like what you have.

See my answer to your other thread : http://www.mathhelpforum.com/math-he...tiplicity.html

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

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

Yes, I have the textbook and teacher's notes but if I understood that there would be no reason to post questions here.

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

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

Good reply.

Thanks