<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-the-discriminant-of-solutions">The Discriminant (# of Solutions) Exercise</a></span></p><p>The <span style="color:#27ae60;">Discriminant</span> is part of the quadratic equation:</p>
<p>$$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$</p>
<p style="text-align: center;">The discriminant $=b^2-4ac$</p>
<p>The cool thing about the discriminant is that it tells us the number of solutions of a quadratic equation that is set equal to zero. There are three possible scenarios:</p>
<p>If $b^2-4ac>0$, the quadratic equation has two solutions.</p>
<p>If $b^2 -4ac=0$, the quadratic equation has one solution.</p>
<p>If $b^2-4ac<0$, the quadratic equation has zero solutions.</p>
<p>The reason why a negative discriminant has zero solutions comes from our earlier arithmetic knowledge. Recall that we cannot have a negative value under a radical.</p>