A quadratic equation always has two roots if complex roots are included and a double root is counted for two. We could have a family like this. If there is no real solution there are two complex solutions.
Anything in the form f xa x-h2k or f xax2bxc will have infinitely many solutions.
The discriminant reveals what type of roots the equation has. We say that any equation that has the form ax 2 bx c 0 or an equation that we can reduce to this form is a quadratic equation. If there is only one solution one says that it is a double root. As we have seen there can be 0 1 or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign b2 - 4ac is positive negative or zero.