The quadratic formula says that any quadratic equation of the form ax^2 + bx + c, then
x=(-b ± √(b^2 - 4ac))/2a, and so because of the square root, theres
obviously going to be no x-intercepts if b^2 - 4ac is negative, one
x-intercept if its zero, or two if its positive. So to calculate the
discriminant, which is whether it has an intercept, no intercepts or two
intercepts is:
∆=b^2 - 4ac, where delta, the greek equivalent of D, is used to represent the discriminant.
In the above equation a=-4, b=3 and c=-2, so
∆=3^2 - 4-4-2=9 - 32=-23, so because the discriminant is negative, then there are no x-intercepts.
This is from
https://answers.yahoo.com/question/index;_ylt=A0LEVvH2KJ5Y8UMAhHwPxQt.;_ylu=X3oDMTByMjB0aG5zBGNvbG8D...
