I want to calculate roots of a polynomial whose coefficients are functions of x where x assume values between an interval

Let x =[0:1:10]; polynomial = [ 1 sin(x) x.^3 x]; let v1,v2 and v3 be the three roots of given polynomial in v whose coefficients are functions of x. I want to plot a graph between v1 and x.

[Jan]

What is "a graph between v1 and x", if x is a vector? How do you define one polynomial with "[1 sin(x) x.^3 x]", is x is a row vector? Do you really mean a [1x34] vector to define a polynomial of the degree 33?

[Matt J]

I want to plot a graph between v1 and x.

OK, the mission is clear. What have you done so far and what problems are you encountering?

[ASHA RANI]

>> x = pi/18;
>> p = [1 sin(x) x.^3 x];
>> r = roots(p)

r =

    -0.6196          
     0.2230 + 0.4816i
     0.2230 - 0.4816i

>> v1 =r(1,1)

v1 =

     -0.6196

[ASHA RANI]

if we take a single value for x, we get v1. But x assume all values between a given interval and we will want to get corresponding v1 and plot between x and corresponding value of x

[ASHA RANI]

> x = [0:pi/18:pi/6]

x =

           0    0.1745    0.3491    0.5236

>> p = [1 sin(x) x.^3 x];
>> r = roots(p)

r =

     0.8999 + 0.3217i
     0.8999 - 0.3217i
     0.6749 + 0.8031i
     0.6749 - 0.8031i
     0.2643 + 0.9220i
     0.2643 - 0.9220i
    -0.3081 + 0.8491i
    -0.3081 - 0.8491i
    -0.8635 + 0.2723i
    -0.8635 - 0.2723i
    -0.6675 + 0.6335i
    -0.6675 - 0.6335i

in this ans of r, which one is represented v1 corresponding to pi/18?

[John D'Errico]

So why did you set x=pi/18?

You were asked to solve this problem for x varying from 0 to 10, NOT just at one value of x.

If the polynomial has three roots, what does v1 versus v2 and v3 mean? Roots need not be provided in any specific order. So how are you supposed to choose v1?

Answer 1

[Matt J]

You cannot use ROOTS on multiple polynomials at a time. You will have to use a loop over x(i),

for i=1:numel(x)

   p =[1 sin(x(i)) x(i).^3 x(i)];

   r{i}=roots(p);

   %More code...

 end

[ASHA RANI]

I got error of this type after running this loop ??? Cell contents assignment to a non-cell array object.

[Matt J]

clear 'r' from memory first, or better yet pre-allocate,

   r=cell(1,numel(x));

[ASHA RANI]

thank you,sir I am sending my original problem in which I want to plot between v1 and corresponding x. please help it