Finding Polynomials From Their Known Roots In Matlab®(Illustrated Expression)

We explained the finding roots of a polynomial in Matlab® here. Also, you can do the same thing in the reverse direction. You can find polynomes from their roots in Matlab® with the ‘poly()’ command. Here, we explained how to find a specific polynomial from its known roots with the ‘poly()’ command in Matlab®, with a very basic example.

How To Use ‘poly()’ Command In Matlab®?

>> a = [0 2 1-j 1+j]
b = poly(a)
c = poly([1 3 3-j 3+j]);
d = poly(c)

a =

  Columns 1 through 2

   0.0000 + 0.0000i   2.0000 + 0.0000i

  Columns 3 through 4

   1.0000 - 1.0000i   1.0000 + 1.0000i


b =

     1    -4     6    -4     0


d =

  Columns 1 through 4

           1           0       -2867       39486

  Columns 5 through 6

      607180     -643800

>> 

To find a polynomial from its known roots in Matlab®, you need to define all the roots in a vector. For example, we defined 4 roots of a polynomial in vector ‘a’ above. What we did is, we typed the polynomial ‘a’ into the poly() command, then assigned it to a variable ‘b’. As you see above again, the result. This vector ‘b’ represents the unknown polynomial that is calculated from its roots.

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Also, you can directly type all the roots inside the parenthesis of poly() command in Matlab®.

The logic of these results that represent polynomials, all the elements represents the coefficients of the polynomial that has one variable. For example result, ‘b’ represents the polynomial of x^4-4x^3+6x^2-4x^. All the coefficients are represented by an element in vectors ‘b’ and ‘d’, from left to right.

Finding out unknown polynomial from its known roots is very easy like above with the ‘poly()’ command in Matlab®.

Conclusion

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This article is prepared for completely educative and informative purposes. Images used courtesy of Matlab®

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