Question 71857: Begging for help.
Find all roots of the polynomial x3 - x2 + 16x -16
Possible answers:
1, 4, -4
. -1, 4, -4
. -1,4i, -4i
.1, 4i, -4i
where did the i come from, what does this represent? Someone please explain how to solve this problem
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find all roots of the polynomial x^3 - x^2 + 16x -16
Possible answers:
1, 4, -4
. -1, 4, -4
. -1,4i, -4i
.1, 4i, -4i
where did the i come from, what does this represent?
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The coefficients add up to zero so x=1 is a root.
Using synthetic division find the other factor:
1....1....-1....16....-16
......1.....0.....16...|..0
Quotient: x^2+16
Remainder: 0
Now find the roots of x^2+16
It factors as (x+4i)(x-4i)=0
x=-4i or x=-4i, or x=1 (these are all the roots of the original cubic)
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The "i" is the square root of negative 1.
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Cheers,
Stan H.
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