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 on 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.