A **quadratic equation** is a second-degree **algebraic equation** that can be expressed in the form:

$$ax^{2}+bx+c=0$$

where,

xā variable, unknown;

a, b, cā coefficients, constants, numbers.

The **solution formula** for the quadratic equation is:

$$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$$

In the solution formula for the quadratic equation, the expression under the square root sign is called the **discriminant**:

$$D=b^{2}-4ac$$

A reduced quadratic equation is a quadratic equation with a coefficient of 1 for the quadratic term:

$$x^{2}+px+q=0$$

The **solution formula** for the reduced quadratic equation is:

$$x=-\frac{p}{2} \pm \sqrt{\left ( \frac{p}{2} \right )^{2}-q}$$