Question #6761

# What are the formulas to solve a quadratic equation?

A quadratic equation can be solved in two steps (calculation of discriminant and roots). The solutions of this equation are called the roots. A quadratic equation may have one or two roots.

Let's consider the following equation in its standard form:

﻿﻿

Step 1. Calculate the discriminant given by the following formula:

﻿﻿

Step 2. Calculate the roots according to the sign of the discriminant ( ﻿﻿ )

Case 1: if ﻿﻿ then the quadratic function has two distinct real roots:

﻿﻿

Case 2: if ﻿﻿ then the quadratic function has one repeated real root:

﻿﻿

Case 3: if ﻿﻿ then the quadratic function has two distinct complex roots:

﻿﻿

Example:

Let's consider the following quadratic equation:

﻿﻿

Parameters of the equation are:

﻿﻿

The discriminant is given by:

﻿﻿

The discriminant is positive, thus the quadratic equation has two distinct real roots given by:

﻿﻿

﻿﻿

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