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Find a polynomial of given degree with given zeros: complex zeros

Find a polynomial of given degree with given zeros: complex zeros-example-1
User Cliabhach
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Solution

For this case we have the following roots:

4 (multiplicity 2) and i

Therefore we can create the following expression


(x-4)(x-4)(x-i)(x+i)

Solving we have:


(x^2-8x+16)(x-i)(x+1)=(x^(2)-8x+16)(x^(2)+1)
x^(4)+x^(2)-8x^(3)-8x+16x^(2)+16

Simplifying we got:


x^4-8x^(3)+17x^2-8x+16

User OregonJeff
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