SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. (InterAct Math # 17) Degree 3: zeros: 1 + i and -10

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Question 1095664: Form a polynomial f(x) with real coefficients having the given degree and zeros. (InterAct Math # 17)
Degree 3: zeros: 1 + i and -10
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

If a polynomial has real coefficients, then complex roots occur in conjugate pairs. So if 1+i is a root, then 1-i is another root. So the three roots are 1+i, 1-i, and 10. Then the polynomial is
%28x-%281%2Bi%29%29%28x-%281-i%29%29%28x-10%29
%28%28x-1%29-i%29%28%28x-1%29%2Bi%29%28x-10%29
%28x%5E2-2x%2B1%2B1%29%28x-10%29
%28x%5E2-2x%2B2%29%28x-10%29
x%5E3-10x%5E2-2x%5E2%2B20x%2B2x-20
x%5E3-12x%5E2%2B22x-20

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
The three roots are 1+i, 1-i, and -10.  Then the polynomial is

%28x-%281%2Bi%29%29%28x-%281-i%29%29%28x-%28-10%29%29

%28%28x-1%29-i%29%28%28x-1%29%2Bi%29%28x%2B10%29

%28x%5E2-2x%2B1%2B1%29%28x%2B10%29

%28x%5E2-2x%2B2%29%28x%2B10%29

x%5E3+%2B+10x%5E2+-+2x%5E2+-+20x+%2B+2x+%2B+20

x%5E3+%2B+8x%5E2+-+18x+%2B+20