Question

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!!

Answer 1

They want to know the:

remaining zeros of f

Answer 2

complex roots come in pairs, so the others must be -i and 9-i.

Algebra I, I believe.

Answer 3

The reason they specify real coefficeints is so that you know the complex roots come in conjugate pairs. Otherwise, it is not true, since

(x-3)(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.