Question 93876: Need to state the roots and completely factor the following:
f(x)= x^5+x^4-9x^3-5x^2-36
OMG - HELP
Thanks
LLo
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Need to state the roots and completely factor the following:
f(x)= x^5+x^4-9x^3-5x^2-36
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I graphed it and found roots at x=-3,x=-2,x=3
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Then using synthetic division to find the remaining factors I got:
-3)....1....1....-9....-5....0....-36
.........1...-2....-3....4....-12...|..0
-2).......1....-4....5....-6..|..0
3)..........1....-1...2...|..0
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So the remaining quadratic factor is x^2-x+2
Using the quadratic formuls I get:
x = [1+-sqrt(1-8)]/2
x = [1+-isqrt7]/2
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So all the roots are x=-3, x=-2, x=3, x= (1+isqrt7)/2, x= (1-isqrt7)/2
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All the factors are (x+3),(x+2), (x-3),(x-(1+isqrt7)/2), (x-(1+isqrt7)/2)
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Cheers,
Stan H.
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