Question 679753
Discriminant!  If zero, then one intercept.  If positive, then two intercepts.  If negative, then no intercept. 

For quadratic {{{ax^2+bx+c}}}, the discriminant is {{{b^2-4ac}}}.
Your given polynomial is {{{2X^2-3X+2}}}, so the values to use are b=-3, a=2, c=2.  Use the values and find the value of the discriminant...