Question 1095091: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other zero(s).
i, 7 square root of 11
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If a polynomial has rational coefficients, then irrational and complex roots must occur in conjugate pairs.
In case you aren't familiar with the term conjugate pairs, the conjugate of the complex number a+bi is a-bi; the conjugate of the irrational number a+b*sqrt(c) is a-b*sqrt(c).
So in your example, with one root i, another root must be -i; and with one root 7*sqrt(11), another root must be -7*sqrt(11).
The four roots are the conjugate pairs
(1) i and -i
(2) 7*sqrt(11) and -7*sqrt(11)
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