Zeros of a polynomial - Math Central

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Question from Gavin, a parent:

Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i

Using this info, answer the following.

a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?

p.s. I used _ for subscript
thanks so much

Gavin,

The solution to this problem relies on two facts. First a polynomial of degree 9 has at most 9 zeros. Second if a polynomial has real coefficients and a + bi is a zero then so is a - bi.

Harley

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