form a 5th degree polynomial f(x) with real coeffcients having the given zeros: 4;-i;4+i must show work donot enter the polynomial in factored form, multiply it out

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mlehuzzah | Student, Graduate | (Level 1) Associate Educator

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If the polynomial has real coefficients, then either the zeros are real, or they come in complex conjugate pairs.  So, for example, if 4+i is a root, then 4-i must be a root as well.  Thus, our polynomial must have the following roots:

4, -i, i, 4+i, 4-i

We can find a polynomial with these roots by multiplying out:


It will be easier to do this in stages:





Thus we want to multiply:





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