SOLUTION: Find an nth degree polynominal function with the real coefficient satisfying the given conditions. n=3;-2 and -2+3i are zero;leading coefficient is 1

Question 262915: Find an nth degree polynominal function with the real coefficient satisfying the given conditions.
n=3;-2 and -2+3i are zero;leading coefficient is 1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find an nth degree polynominal function with the real coefficient satisfying the given conditions.
n=3;-2 and -2+3i are zero;leading coefficient is 1
:
x = -2; gives us a factor of (x+2)
:
x = -2 + 3i
x + 2 = 3i
Square both sides
(x+2)^2 = (3i)^2
FOIL the left
x^2 + 2x + 4 = 9(i^2)
x^2 + 2x + 4 = 9(-1)
x^2 + 2x + 4 = -9
x^2 + 2x + 4 + 9 = 0
(x^2 + 2x + 13); the other factor
:
(x+2)*(x^2+2x+13) = x^3 + 4x^2 + 17x + 26
:
f(x) = x^3 + 4x^2 + 17x + 26
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