Question

Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation.
Provide a unique example to back up your explanation, please help

Answer 1

Let the discriminant by denoted by D.
\[D:=b2−4ac\]

Which corresponds to the general quadratic equation:
\[ax2+bx+c=0\]
where a,b and c are real numbers.

Recall that the solutions of this general quadratic equation are given by
\[x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\]

If
\[b2−4ac<0\]
then the quadratic has no real solutions (actually, has two complex conjugate pairs.
If
\[b2−4ac=0\]
then the quadratic has one distinct (i.e. one and only one) real solution, i.e.\[x \in \mathbb{R}\]

If \[b^2-4ac >0\] then the quadratic has two distinct real solutions.