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How to Solve Polynomial Equation in Excel (5 Simple Methods)

In this tutorial, I am going to show you 5 simple methods to solve a polynomial equation in excel. You can use these methods to solve simple polynomial equations quickly and efficiently. I will also provide a practice workbook which you can download for some hands-on actions.


Download Practice Workbook

You can download the practice workbook from here.


5 Simple Methods to Solve Polynomial Equation in Excel

To keep this tutorial simple and clear, we will use polynomial equations up to the third order. Again, that is to easily explain the steps. These methods can be applied to higher-order polynomials as well. how to solve polynomial equation in excel


1. Using Goal Seek Option

If you know the result of a polynomial, then you can use the Goal Seek feature to find the input which produces that result. We can use this feature to solve a polynomial equation in excel.

Steps:

  • First, Double-click on cell B7 and enter the following formula:
=(5*C7^3)-(2*C7^2)+(3*C7)-6
  • Then, give any value for X in cell C5.

entering the polynomial equation formula to solve

  • Next, go to the Data tab and then to Forecast.
  • Here, under What-If Analysis, click on Goal seek.

opening the goal seek tool to solve polynomial equation in excel

  • Next, enter the values as in the image below and press OK.


2. Utilizing Solver Feature

The Solver tool in excel uses operations research methods to find the optimal solution from a set of equations. This tool is very helpful to solve any polynomial equation in excel.

Steps:

  • To begin with, open the Solver tool under the Data tab.

opening the solver tool to solve polynomial equation in excel

  • Then, type in the following parameters in the Solver Parameters window as in the image below.

solver parameters to solve polynomial equation in excel

  • Finally, click on Solve and the Solver will calculate the value of X.

Read More: How to Solve an Equation for X When Y is Given in Excel


3. Solving Quadratic Polynomials Equation

Among the polynomial equation types, quadratic is probably the most common. We can solve any quadratic polynomial equation using a simple formula in excel.

Steps:

  • First, click on cell C9 and enter the below formula:
=(-C7+SQRT(C7^2-4*C6*C8))/(2*C6)

entering the formula to solve quadratic polynomial equation

  • Similarly, type the below formula in cell C10:
=(-C7-SQRT(C7^2-4*C6*C8))/(2*C6)

  • Now, if you press the Enter key, you should see the solutions of X.

Read More: Solve Quadratic Equation in Excel VBA (with Quick Steps)


4. Finding Solution of Multivariable Equation by MINVERSE Function

Originally, the MINVERSE function in excel returns the inverse of a given array. But, we can use this function to solve a multivariable polynomial equation. Our equations are as follows:

3x+2y+z=8

11x+-9y+23=27

8x-5y=10

Steps:

  • First, select the cells from B10 to D12 and type in the following formula:
=MINVERSE(B5:D7)
  • Now, press Ctrl+Shift+Enter and you will see the respective inverse values.

entering the MINVERSE formula to solve polynomial equation in excel

  • Then, select the cells from F10 to F12 and enter the following formula:
=MMULT(B10:D12,E5:E7)
  • Finally, again press Ctrl+Shift+Enter and you should get the values of x, y, and z.

Read More: Solve Algebraic Equations with Multiple Variables (3 Ways)


5. Using Solver to Find Solution of Multivariable Equation

In this method, we will be using the Solver tool in excel to solve a polynomial equation in excel. We are using the same 3 equations from the previous method.

Steps:

  • First, double-click on cell E5 and type in the formula below:
=3*C5+2*C6+C7

entering polynomial equation formula to solve in excel

  • Now, click on cell F5 and enter this formula:
=FORMULATEXT(E5)
  • Again, copy this formula to the cells below.

show the formula text to solve polynomial equation in excel

  • Next, open the Solver tool as we showed before and enter the parameters as shown below.
  • Now, to add the Constraints, click on Add.

  • Next, in the Add Constraint window, add the above constraints in a similar way.
  • Note that, you need to click on Add after entering each constraint.

  • Finally, click on the Solve option as we saw previously and you should see the solutions.

Read More: How to Solve 2 Equations with 2 Unknowns in Excel (2 Examples)


Things to Remember

  • Remember, you have to press Ctrl+Shift+Enter at the same time and not only Enter where we mentioned them.
  • Make sure to insert the parentheses exactly as we showed, otherwise the formula might not work.
  • If you do not have the Solver tool showing under the Data tab, then you can bring it easily by clicking on this link.

Conclusion

I hope that you understood all of the above methods on how to solve a polynomial equation in excel. If you really comprehend the steps, then you should be able to apply them in a variety of scenarios. Also, whenever you get stuck in any step, then I would recommend going through them a few times. Lastly, to learn more excel techniques, follow our ExcelDemy website. If you have any queries, please let me know in the comments.


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Nazmul Hossain Shovon

Nazmul Hossain Shovon

Hello, I am Nazmul Hossain. I am currently working full-time in Exceldemy as an Excel & VBA Content Developer. I have completed my bachelors in Naval Architecture and Marine Engineering from Bangladesh University of Engineering and Technology. I am interested in working with MS Excel. I also like coding web applications a lot.

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