Posted by Breanna on Sunday, December 30, 2012 at 5:31am.
information is given about a polynomial f(x) whose coeffiecients are real numbers. Find the remaining zeros of f.
degree4, zeros i, 9+i
**I am just not getting these coefficients. I know that there has to be an easier way to learn this. Please help!!

calculus  Breanna, Sunday, December 30, 2012 at 5:33am
They want to know the:
remaining zeros of f

calculus  Steve, Sunday, December 30, 2012 at 6:01am
complex roots come in pairs, so the others must be i and 9i.
Algebra I, I believe.

calculus  Steve, Sunday, December 30, 2012 at 6:04am
The reason they specify real coefficeints is so that you know the complex roots come in conjugate pairs. Otherwise, it is not true, since
(x3)(x+i) = x^2  3x + ix  3i
= x^2 + (3+i)x  3i
which is a perfectly useful quadratic, but its coefficients are not real, so the roots do not have to come in conjugate pairs.
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