In the Quadratic Formula, what does it mean if $b^2-4ac>0$, $b^2-4ac<0$, and $b^2-4ac=0$? Concerning the Quadratic Formula:
What does it mean if  $b^2-4ac>0$, $b^2-4ac<0$, and $b^2-4ac=0$?

Since one has the term $\sqrt{b^2-4ac}$ in solution of the quadratic formula, if $b^2-4ac>0$, then the equation has two real solutions (since $\sqrt{b^2-4ac}$ is real, and $b$ and $2a$ are also real). When $b^2-4ac<0$, then the quadratic equation has two complex solutions (since $\sqrt{b^2-4ac}$ is complex imaginary). If $b^2-4ac=0$, then $\sqrt{b^2-4ac}=0$, implying that the solution is $x=\dfrac{-b}{2a}$ (can you see why?).
