# Discriminant

## Definition

The value obtained from the subtraction of square of the coefficient of first degree term from four times the product of coefficients of second degree and zero degree terms of a quadratic equation is called the discriminant of a quadratic equation.

For example, $ax^2+bx+c = 0$ is a quadratic equation in standard form and it is formed by three unlike terms.

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

The value obtained from $b^2 \,–4ac$ is called the discriminant of the second degree polynomial $ax^2+bx+c = 0$.

### 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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