Question

How do you find the discriminant and how many solutions does `4x^2-4x+11=0` have?

Answer 1

The discriminant is given as:
`Delta=b^2-4ac`
In your equation (written in the general form: `ax^2+bx+c=0`) you have:
`a=4`
`b=-4`
`c=11`
So: `Delta=(-4)^2-4*(4*11)=-160<0` This means that you cannot have REAL solutions to your equation (however, you can have two COMPLEX solutions!).