Surely this isn't the whole question? If "X^2= Y" then X^3= XY so that X^3- YX+ 0= 0. The coefficient of X^2 and the constant term are 0.
If "X^3+ PX^2+ Q= 0" with P= -1 and Q= 20, so X^3- X^2+ 20= 0. If X= -2, X^3- X^2+ 20= -8- 4+ 20= 12. If X= -3, X^3- X^2+ 20= -27- 9+ 20= -16 so there is a root between -3 and -2. The other two roots are not real numbers. What does that have to do with "Y"?