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Mathematics 45 Online
OpenStudy (anonymous):

Is there a way to find the number of roots of a polynomial without finding the roots?

OpenStudy (anonymous):

yes Descartes rule of signs http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs

OpenStudy (anonymous):

Number of Roots = Degree Of Polynomial...

OpenStudy (anonymous):

There will be as many roots of the polynomial as there is the highest power of that polynomial...

OpenStudy (anonymous):

Then, do I need to use Descartes Rule of Signs or just look at the highest degree?

OpenStudy (anonymous):

Degree means highest power just look for the highest power...

OpenStudy (anonymous):

Great! You've saved the day! Thanks!

OpenStudy (anonymous):

Welcome dear...

OpenStudy (anonymous):

you are getting answers to two different questions

OpenStudy (anonymous):

One is to find simply how many roots are there... Other is to find out of those roots which are positive negative and complex that is explained by Descartes Rule...

OpenStudy (anonymous):

one question is how many zeros (roots) does a polynomial of degree \(n\) has and the answer is it has \(n\) roots counting multiplicity HOWEVER these roots need not be real numbers! if the question is how many REAL roots a polynomial has, Descartes rule of sign can help answer that question, but does not in fact answer it

OpenStudy (anonymous):

Will you please explain what is the multiplicity what is its concept @satellite73 ??

OpenStudy (anonymous):

if you have a specific question we could work throught it @waterineyes for the polynomial \((x-2)^3(x+1)\) the root 2 is a zero with multiplicity 3

OpenStudy (anonymous):

Here in this example how do you calculated 3 as its multiplicity??

OpenStudy (anonymous):

Suppose I have: \[(x-1)^5(x-3)^2(x-2)(x+5) = 0\] Here explain the concept of multiplicity @satellite73

OpenStudy (anonymous):

the zeros of your polynomial are 1, 3, 2 and -5 the multiplicity of 1 is 5, the multiplicity of 3 is 2 and 2 and -5 have multiplicty 1

OpenStudy (anonymous):

It is related to powers.. Am I right?? For \((x+5)^{10}\) Root : -5 with, Multiplicity = 10 right @satellite73

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