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.

How to Solve Polynomial Equation in Excel: 5 Simple Methods

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.

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 that 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.

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

• 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.

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

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

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)`

• 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.

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.

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

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`
• Then, copy this formula to the cells below by Fill Handle.

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

• Next, open the Solver tool as we showed before and enter the parameters as shown below.

• Next, in the Add Constraint window, add the above constraints similarly.
• 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.

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.

Conclusion

I hope that you understand 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, I would recommend going through them a few times. If you have any queries, please let me know in the comments.

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Nazmul Hossain Shovon

Nazmul Hossain Shovon, a BUET graduate in Naval Architecture and Marine Engineering, embarked on his career with 8 months dedicated to the Exceldemy project's triumph. Transitioning into a Software Developer role, he specialized in web add-in development. At Exceldemy, he authored about 125 blog articles and solved many visitorsâ€™ problems, refining his writing skills and delving into Excel-related topics. With a primary passion for programming and software development, Shovon continually explores new horizons, fostering professional growth in his... Read Full Bio

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