# Can we calculate the roots of polynomials with matrix coefficients?

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Benson Gou on 30 Aug 2019
Answered: Nikhil Sonavane on 6 Sep 2019
Dear All,
I have a polynomial which has matrix coefficients. For example, I have the following equation:
[1 0;0 1]*[x_1^2; x_2^2] + [2 0;0 2]*[x_1; x_2] + [1 0; 0 1] = [0; 0]
It is obvious that that solution is x_1 = -1; x_2 = -1.
But if the coefficient matrices are general, how can we obtain the solution in Matlab?
Thanks a lot.
Benson

the cyclist on 30 Aug 2019
When you say the coefficient matrices are "general", do you mean that they are not necessarily diagonal?
Benson Gou on 30 Aug 2019
Yes, the coefficient matrces are Not necessraily diagonal matrices. Those matrices could be a very gerneal matrix. However, all of them are square matrices.
Thanks a lot.
Benson

Nikhil Sonavane on 6 Sep 2019
You can use solve function to solve the system of equation in two variables. You may refer to its documentation for more information.