the discriminant is the bit under the squaer root sign in the quadratic formula
when you have ax^2+bx+c=0 the discriminant is [tex] b^{2}-4ac [/tex] if discriminant>0 then have 2 real solutions/roots discriminant=0 then have 1 real solution/root discriminat<0 then have no real roots (2 imaginary roots)
-3x^2+x-1=0 a=-3 b=1 c=-1
[tex] 1^{2}-4(-3)(-1) [/tex]=1-12=-11 -11<0 has zero real solutions
