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

Answer 1

Perhaps you should first identify the discriminant's equation.

Answer 2

The discriminant is a part of the quadratic formula, namely it is located under the radical:
\[ \color{maroon}{\mathtt{x= \frac{-b \pm \sqrt{\color{goldenrod}{b^2 - 4ac}}}{2a}}} \] Consider the different values that the golden part may take. What would happen if the \(\mathtt{b^2 - 4ac}\) part were negative? What if it was a perfect square, where the radical would be cancelled? When it's not a perfect square and the radical remains? When it is 0?

Some choice points to make are concerning rational roots (fractions of integers), irrational roots (the radical is still there), doubled / one root (\(\pm 0\)) and complex valued \(radical contains negative values).