SOLUTION: P(x)=x^3-5x+2 it ask me to find all the real zeros of the polynomial

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Question 62015: P(x)=x^3-5x+2 it ask me to find all the real zeros of the polynomial
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Descarte's Rule of Signs:
P(x) = (+) x^3 (+-) 0x^2 (-) 5x^1 (+) 2x^0
P(-x) = (-) x^3 (+-) 0x^2 (+) 5x^1 (+) 2x^0
Pos: 2 .. 0
Neg: 1 .. 1
Img: 0 .. 2
We now know that there is definetly a negative zero.
P(x) = x^3 - 5x + 2
a = 1,2
b = 1
+- a/b = +- 1 and +- 2
Synthetic Division:
2.|......1......0......-5......2......
............1......2......-1.......0
(x - 2)(x^2 + 2x - 1) = P(x)
x^2 + 2x - 1 = 0
x^2 + 2x = 1
(x + 1)^2 = 2
x + 1 = +- sqrt(2)
x = -1 +- sqrt(2)
Zeros:
x = 2
x = -1 + sqrt(2)
x = -1 - sqrt(2)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3+-+5x+%2B+2%29