Question

Compute the value of the discriminant and give the number of real solutions of the quadratic equation
-7x^2-8x-3=0

Answer 1

\(ax^2 + bx + c = 0\)

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

\(b^2 - 4ac\) is the discriminant.

If the discriminant is positive, there are 2 different real roots.
If the discriminant equals zero, the is one real root with multiplicity 2.
If the discriminant is negative, there are two complex roots.

Answer 2

mathstudent55 has it right. There's a little more to the discriminant, however. If the discriminant is positive, there are two real roots: that are rational numbers if the discriminant is a perfect square; that are irrational numbers if the discriminant isn't a perfect square.

I created a video that explains the quadratic formula and the discriminant. It may provide additional assistance to you: https://www.youtube.com/watch?v=W0zIsspXh4g