Given the quadratic $\displaystyle ax^2 + bx + c = {\color{red}0}$ (the 0 is important), the discriminant refers to $\displaystyle {\color{blue}b^2 - 4ac}$ which comes from the quadratic equation: $\displaystyle x = \frac{-b \pm \sqrt{{\color{blue}b^2 - 4ac}}}{2a}$

Now, if:

- $\displaystyle b^2 - 4ac > 0$, then there are 2 real solutions to x.
- $\displaystyle b^2 - 4ac = 0$, then there is
**exactly** 1 real solution to x. - $\displaystyle b^2 - 4ac < 0$, then there are
**no** real solutions to x.

See if you can apply this to your quadratics.