Question

What term is ${\mathrm{b}}^2-4\mathrm{ac}$?

Answer 1

Quadratic equations:

1. The polynomial equations of degree $2$ are called quadratic equations.
2. The standard form of a quadratic equation is ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$.
3. It is a second-degree quadratic equation of x.

Quadratic formula:

The solution to a quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ is given by the quadratic formula:

$\mathrm{x}=\frac{-\mathrm{b}\pm \sqrt{{\mathrm{b}}^2-4\mathrm{ac}}}{2\mathrm{a}}$ where $\mathrm{a}\ne 0$.

Components of the formula:

1. The expression ${\mathrm{b}}^2-4\mathrm{ac}$ is called the discriminant of the formula.
2. This term decides the number of real solutions for the given quadratic equation.
3. Hence, it is called the discriminant.

Hence, the term ${\mathrm{b}}^2-4\mathrm{ac}$ is called the discriminant.