SOLUTION: P(x) = x^3 - 2x^2 - 14x + 40 has a zero of 3 + i. Find the remaining zero of P(x).

Question 57638This question is from textbook Applied College Algebra
: P(x) = x^3 - 2x^2 - 14x + 40 has a zero of 3 + i. Find the remaining zero of P(x). This question is from textbook Applied College Algebra

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
P(x) = x^3 - 2x^2 - 14x + 40 has a zero of 3 + i.
Find the remaining zero of P(x).
:
First deal with 3 + i, kind of like the reverse of "completing the square"
x = 3 + i
x - 3 = i
Square both sides
x^2 - 6x + 9 = i^2
x^2 - 6x + 9 = -1
x^2 - 6x + 9 + 1 = 0
x^2 - 6x + 10 = 0
:
Divide the above expression into the original equation:
....................................................x + 4
.....................--------------------------
x^2-6x+10 | x^3 - 2x^2 - 14x + 40
:
use long division: you will get: x + 4 and it comes out even
:
The remaining 0: x = -4

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