# Discriminant of a Quadratic Equation

The subtraction of four times the product of constant and literal coefficient of second degree term from the square of the literal coefficient of the first degree term of the quadratic equation is called the discriminant of the quadratic equation.

## Introduction

$ax^2+bx+c = 0$ is a quadratic equation in standard form. It contains three unlike terms.

1. The first term $ax^2$ is a second degree term and the literal coefficient of $x^2$ is $a$.
2. The second term $bx$ is a first degree term and the literal coefficient of $x$ is $b$.
3. The third term $c$ is a zero degree term and also known as a constant term. The literal coefficient of $x^0$ is $c$.

According to the fundamental definition of the discriminant of a quadratic equation, $b^2-4ac$ is the discriminant of the quadratic equation.

### Representation

The discriminant of a quadratic equation is denoted by either $D$ or $\Delta$ in mathematics.

$D = b^2 \,–4ac \,\,\,$ (or) $\,\,\, \Delta = b^2 \,–4ac$

#### Example

$2x^2+3x+7 = 0$ is a quadratic equation.

Compare this quadratic equation with standard form quadratic equation. Therefore $a = 2$, $b = 3$ and $c = 7$.

Discriminant of this quadratic equation is $\Delta = 3^2 \,–4 \times 2 \times 7$

$\Delta = 9 -56 = -47$

Therefore, the discriminant of the quadratic equation $2x^2+3x+7 = 0$ is $-47$.

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