Question 136536: Given the polynomial function has the given zero, find the other zeros.
f(x) = x^3 - 8x^2 + 17x - 30; 6
Choices are:
a) 1 + square root of 5i, 1 - square root of 5i
b) 1 +2i, 1-2i
c) 1 + square root of 5, 1 - square root of 5
d) -1+2i, -1-2i
I think I have ruled out c - but I can't figure out the imaginary #'s. I don't know if I'm just not thinking clearly, or just forgetting something that I already know.
If you could help me with this, I would greatly appreciate it.
CB
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given the polynomial function has the given zero, find the other zeros.
f(x) = x^3 - 8x^2 + 17x - 30; 6
Choices are:
a) 1 + square root of 5i, 1 - square root of 5i
b) 1 +2i, 1-2i
c) 1 + square root of 5, 1 - square root of 5
d) -1+2i, -1-2i
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If 6 is a zero, x-6 is a factor.
Use synthetic division to find the other factor:
6)....1....-8....17....-30
......1.....-2....5...|...0
Quotient: x^2-2x+5
use the quadratic formula to find the remaining two zeroes:
x = [2 +- sqrt(4-4*5)]/2
x = [2 +- sqrt(-16)]/2
x = [1 +- 2i]
x = 1+2i or x=1-2i or x=6 are the zeroes
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Cheers,
Stan H.
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