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.

- The first term $ax^2$ is a second degree term and the coefficient of $x^2$ is $a$.
- The second term $bx$ is a first degree term and the coefficient of $x$ is $b$.
- 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 $ax^2+bx+c = 0$.

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

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

$2x^2+3x+7 = 0$ 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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