8/17/2019 Finding a Polynomial of a Given Degree With Given
Zeros: Real Zeros
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Kwadwo Amankwa - 04/23/2015 10:00:04 PM PDT
PreCalculus / Amankwa, Kwadwo (Amankwa)
Finding a polynomial of a given degree with given zeros: Real
zeros
Find a polynomial of degree that has the following
zeros.
(multiplicity ) ,
Leave your answer in factored form.
The Factor Theorem tells us the following.
A number is a zero of a polynomial if and only if is a
factor of
We also get that, if is a zero of multiplicity then is a
factor.
We're told that has the zeros shown below on the left.
The Factor Theorem gives the corresponding factors on the
right.
Zero Factor
(multiplicity )
These factors give the following polynomial.
Since this polynomial has degree it is a possible answer. We are
told that we can
leave it in factored form.
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