How to calculate the roots of 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:





A quadratic equation can be solved in two steps (calculation of discriminant and 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:





A quadratic equation can be solved in two steps. 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 

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:





A quadratic equation can be solved in two steps. 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 

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: