Question #6766   Submitted by Answiki on 09/27/2022 at 05:21:13 PM UTC

How to solve an equation like ax^2+bx+c=0?

Answer   Submitted by Answiki on 09/27/2022 at 05:24:37 PM UTC

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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Answer by Answiki on 09/27/2022 at 05:24:37 PM

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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Answer by Answiki on 09/27/2022 at 05:13:06 PM

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:









Answer by Answiki on 09/27/2022 at 05:09:19 PM

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:









Answer by Answiki on 09/27/2022 at 05:06:04 PM

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:






Question by Answiki 09/27/2022 at 04:51:46 PM
How to solve a quadratic equation?
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