Finding zeros of R(x) and nonreal zeros

label Algebra
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Suppose that R(x) is a polynomial of degree 9 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros.

-3, 6, 3i, -2+ 2i

Answer the following.

(a) Find another zero of R(x).

(b) What is the maximum number of real zeros that R(x) can have?

(c) What is the maxium number of nonreal zeros that R(x) can have?

Oct 25th, 2015

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

if 3i is a zero then -3i is also a zero. similarly -2-2i is also a zero

-3, 6, 3i, -2+ 2i,-3i,-2-2i are the zeros

a) -3i is the other zero of R(x)

b) 4 complex as of now and a maximum of 5 real zeros R(x) can have

c) 4 complex zeros and 2 real zeros as of now. There is a possibility of two zeros being complex out of other 3 unknown zeros

So, R(x) can have a maximum of 6 complex zeros

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 25th, 2015

how many zeros would there be for c? it just asks for a number

Oct 25th, 2015

For c, a maximum number of 6 non-real zeros are possible

and a minimum of 3 real zeros

So, 3 Real zeros for c

Oct 25th, 2015

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