# Why is the discriminant useful?

Mar 23, 2018

To determine how many roots are there in a quadratic equation.

#### Explanation:

There are 4 natures

${b}^{2} - 4 a c > 0$ and is a perfect square -># 2 rational roots

${b}^{2} - 4 a c > 0$ and is not a perfect square $\to$ 2 irrational root
${b}^{2} - 4 a c = 0 \to$ 1 root
${b}^{2} - 4 a c < 0$ No root