Struggling with Polynomial Functions: Can Complex Zeros Confuse You?

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SUMMARY

The discussion focuses on constructing a polynomial function with real coefficients that includes the zeros -1, 1+4i, and its conjugate 1-4i. The polynomial must be expressed in standard form and of minimum degree. The factors derived from these zeros are (x + 1), (x - (1 + 4i)), and (x - (1 - 4i)). Multiplying these factors results in the polynomial function: (x + 1)((x - 1)^2 + 16), which simplifies to a polynomial of degree three.

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hw help :( polynomial fxns.

Hey guys and gals, i'd appreciate if you could help me (well) with this question.

Write a polynomial function at minimum degree in standard form with real coefficients whose zeros include -1 and 1+4i

:O its hard for me, I am not a math person, and my precalculus teacher doesn't teach, he just talks.

Thanks!

btw i have a test tomorrow, so if you could tell me the answer and how you got it, that'd be awesome, because then i can study it and learn, thanks!
 
Physics news on Phys.org
If a polynomial is factored to look like this:

(x-a)(x-b)=0

what does that mean?
 
If a is a zero of a polynomial then x-a is a factor.

If a polynomial with real coefficients has 1+4i as a zero then it also has
1- 4i as a root.

If your polynomial has 1, 1+ 4i, and 1- 4i as zero what factors does it have? Multiply them together.
 

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