Form a polynomial f(x) with real coefficients having given degree and zeros.

label Algebra
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Degree 4; zeros: 4-3i; -5 multiplicity 2

Oct 28th, 2015

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(x-(-5))^2(x-(4-3i))(x-(4+3i))=0 is the answer.

The multiplicity of two means that the root is raised to the 2nd power. For complex numbers that are zeros the conjugate of the number is always a zero as well. To get the conjugate of a complex number like 4-3i you just change the sign in front of the term with the i in it. So the conjugate is 4+3i. Then to write the function you just subtract the zeros from x in parantheses for each zero and multiply them all together and set equal to 0.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 28th, 2015

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