How to get polynomial by the given root in MatLab? - poly -- MatLab

How to get polynomial by the given root in MatLab?

[Ans]

poly

[description]

(1)

<pr_coef>=poly(<pr_vec>);

It  will return coefficients of polynomial with specified roots of polynomial.

<pr_coef>

 coefficients of polynomial.

vector type.

<pr_vec>

specified roots of polynomial.

vector type.

(2)

<pr_M>=poly(<M>)

Let M is be a N by N matrix.

pr_M is a row vector with N+1 elements which are the coefficients of the

characteristic polynomial.

It is computed by det(lambda*eye(size(M)) - M).

<pr_M>

pr_M is coefficients of characterist polynomial.

vector type.

<M>

roots of polynomial

Square-Matrix type.

more details on:

Polynomial with specified roots or characteristic polynomial - MATLAB poly (mathworks.com)

code:

clear

clc

pr=[1:6] %root of polynomial

poly1=poly(pr) %cooefficient of polynomial given by pr.

fprintf("1\n");

%{

output:

pr =

1 2 3 4 5 6

poly1 =

Columns 1 through 6

1 -21 175 -735 1624 -1764

Column 7

720

%}

%means the polynomial is:x^6-21*x^5+175*x^4-735*x^3+1624*x^2-1764*x+720=0

pr_M=[1 3 4 4;4 6 7 8; 3 7 8 9; 2 7 9 3]

poly_M=poly(pr_M)

rootPoly_M=roots(poly_M)%get root of pr_vec.

fprintf("2\n");

%{

output:

pr_M =

1 3 4 4

4 6 7 8

3 7 8 9

2 7 9 3

poly_M =

1.0000 -18.0000 -111.0000 -75.0000 -37.0000

rootPoly_M =

22.9762 + 0.0000i

-4.2859 + 0.0000i

-0.3452 + 0.5066i

-0.3452 - 0.5066i

%}