## pre calc: make poly of deg 4 with roots x = i-2, 1-i

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
seth
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### pre calc: make poly of deg 4 with roots x = i-2, 1-i

Make a Polynomial of degree 4 that has roots x= i-2, 1-i

i have no idea what to do

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: pre calc: make poly of deg 4 with roots x = i-2, 1-i

Make a Polynomial of degree 4 that has roots x= i-2, 1-i

i have no idea what to do
Do like they explain in this lesson. The fact that zeroes are complexes means that there were negatives inside the square roots when they did the Quadratic Formula. The Quadratic Formula does plus/minus before the square root part, so you know you have the other-sign version of each of the zeros:

for x = -2 + i, you also have x = -2 - i
for x = 1 - i, you also have x = 1 + i

For any root x = a, you have the factor x - a. So create the pairs of factors, and multiply them together to get the original two quadratics. Then multiply the two quadratics to get the degree-4 poly.

If you get stuck, please write back showing what you did. Thanks!