Solving Polynomial Equations Using Matlab

Polynomial equations are some of the most popular types of equations in Math. Knowing how to solve them is a thing but actually solving them is another thing.

The methods you can use to solve them are many, but if you happen to have Matlab or the free Matlab alternative Octave you might as well be good using them to buy time if the purpose of solving the equation is more than simply solving the equation.

Caution: The following methods will help you solve polynomial equations quickly but will not show you how to manually solve polynomial equations, it will simply help you get results faster. This can be helpful if you are not interested in the method but on the answers and may also be very useful to check your result after manually solving your equations.

Solving polynomial equations using Matlab

Solving quadratic equations using Matlab

Quadratic equation are equations in the form




So you will also find quadratic equations in the form




Let’s go ahead and solve the following equation with Matlab


To solve this equation with Matlab you will enter the following code

roots([1 -3 2])

and Matlab will give you the roots of the polynomial equation


If the equation was the following


the code would be

roots([1 0 -4])

and the result


Solving cubic equations using Matlab

Let’s use the following equation


The line of code to solve it won’t be that different compared to the previous one. The only difference here is that we have non-zero third-order coefficient to add to it

roots([1 6 0 -20])

Do not forget to add 0 between 6 and -20 since the first-order coefficient is zero

The result will be


Solving quartic equations using Matlab

Using the following polynomial equation


The code will be

roots([1 2 -6*sqrt(10) +1])

And the result will be


The higher-order the higher number of coefficients. Remember the order which with you enter coefficients in the code affect the result, and always remember to put 0 to indicate where the coefficient is not existent for lower exponents of the equation.

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