Finding a polynomial of a given degree with given zeros

label Algebra
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Finding a polynomial f(x) with a degree of 3 with real coefficients and the following zeros.

-4, -3+i

Simplify completely including i's.

Oct 22nd, 2015

Thank you for the opportunity to help you with your question!

If -3+i is a zero then the conjugate -3-i is also a zero to have a real polynomial so :

f(x)=(x-(-4))(x-(-3+i))(x-(-3-i))=(x+4)(x^2-x(-3-i-3+i)+(-3+i)(-3-i))=(x+4)(x^2+6x+10)

f(x)=x^3+6x^2+10x+4x^2+24x+40=x^3+10x^2+34x+40

Good Luck !!!

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 22nd, 2015

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