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

May 6, 2015

The discriminant is given as:
$\Delta = {b}^{2} - 4 a c$
In your equation (written in the general form: $a {x}^{2} + b x + c = 0$) you have:
$a = 4$
$b = - 4$
$c = 11$
So: $\Delta = {\left(- 4\right)}^{2} - 4 \cdot \left(4 \cdot 11\right) = - 160 < 0$ This means that you cannot have REAL solutions to your equation (however, you can have two COMPLEX solutions!).