SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 3; zeros: -3 and 3 - 2i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 3; zeros: -3 and 3 - 2i      Log On


   

Question 1050756: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree: 3; zeros: -3 and 3 - 2i
Found 2 solutions by ewatrrr, josgarithmetic:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
[x -(3-2i)][x -(3+2i)] = [x -3 + 2i][x-3 -2i] = (x-3)^2 -(2i)^2 = x^2-6x + 9 + 4
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(x+3)(x^2 - 6x + 13) = x^3 - 6x^2 + 13x + 3x^2 - 18x + 39 = x^3-3x^2 - 5x + 39
Check Arithmetic

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The other complex zero of 3%2B2i is needed.

f%28x%29=%28x-%28-3%29%29%28x-%283-2i%29%29%28x-%283%2B2i%29%29

%28x%2B3%29%28x-3%2B2i%29%28x-3-2i%29

%28x%2B3%29%28%28x-3%29%2B2i%29%28%28x-3%29-2i%29

%28x%2B3%29%28%28x-3%29%5E2-%28-1%294%29

%28x%2B3%29%28x%5E2-6x%2B9%2B4%29

%28x%2B3%29%28x%5E2-6x%2B13%29

x%5E3-6x%5E2%2B13x%2B3x%5E2-18x%2B39

highlight%28x%5E3-3x%5E2-5x%2B39%29