SOLUTION: Find all zeros exactly for the following polynomial: 2x^3-5x^2-2x+2 Can someone go through this step-by-step with me to help me understand the logic?

Question 1021433: Find all zeros exactly for the following polynomial:
2x^3-5x^2-2x+2
Can someone go through this step-by-step with me to help me understand the logic?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2x^3-5x^2-2x+2
the zeros to test are +/-2 and +/-1, and +/- 1/2, the quotient of the factors of constant 2 at the right end and 2 at the left end.
With synthetic division, neither a or 2 with either sign works.
Try 1/2
(1/2)/2===-5====-2===2
;;;;;2=====-4====-4==0
x=1/2 is a root.
the factors are (x-1/2) and (2x^2-4x-4), which reduces to x^2-2x-2.
That needs the quadratic equation.
x=(1/2)(2+/-sqrt(4+4))=(1/2(2+/-2 SQRT (3)) SINCE SQRT 12=2 SQRT 3.
x=1+/-sqrt(3)
Those are the other two roots.
1/2, 1+sqrt (3), 1- sqrt (3)

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