SOLUTION: Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i f (x) = _____ Appreciate help on this question. I believe it is asking for zeros,

Question 1068321: Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i
f (x) = _____
Appreciate help on this question. I believe it is asking for zeros, only two zeros given, need to find the third zero. ( think that is what this question is asking). Need step-by-step solution.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i
:
from the zeros given we can make two factors
x = 4
(x-4) = 0
and
x = 3 + i
x - 3 = i
Square both sides
(x-3)^2 = i^2
FOIL (x-3()x-3), i^2 is -1
x^2 - 6x + 9 = -1
x^2 - 6x + 9 + 1 = 0
x^2 - 6x + 10 = 0
Make an equation using these two factors
f(x) = (x-4)*(x^2-6x+10)
multiply these two factors, results:
f(x) = x^3 - 10x^2 + 34x - 40
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