SOLUTION: Find all roots of f(x) = x^3-x^2-5x+5 EXACTLY. Sketch a complete graph of f(x) and label all roots clearly.

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Question 441117: Find all roots of f(x) = x^3-x^2-5x+5 EXACTLY. Sketch a complete graph of f(x) and label all roots clearly.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all roots of f(x) = x^3-x^2-5x+5 EXACTLY. Sketch a complete graph of f(x) and label all roots clearly.
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Since the sum of the coefficients is zero x= 1 is a root.
Use synthetic division to find the other two:
1)....1....-1....-5....5
.......1.....0.....-5...|..0
Quotient: x^2-5
Factor x^2-5 = 0
(x-sqrt(5))(x+sqrt(5)) = 0
x = sqrt(5) or x = -sqrt(5) or x = 1
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Cheers,
Stan H.
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