You can put this solution on YOUR website! The Rational Root Theorem tells you that if the polynomial has a rational zero then it must be a fraction p/q, where p is a factor of the last constant and q is a factor of the first coefficient.
Since both the first and the last coefficients are 2 the factors are 1 & 2
The possible rational roots are +- 1/2, 1, 2
If you test them all you will find that -2 is the only rational root. (Answer) If you use long division (2x^3-7x+2)/(x+2)=2x^2-4x+1. Then if you use the quadratic formula on this result it gives the other 2 irrational roots (2-sqrt(2)/2) and (2+sqrt(2))/2.
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Ed
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