find roots in matlab

Matlab provides several built-in functions to find the roots of a given polynomial equation.

One of the functions that can be used to find the roots of a polynomial is roots(). Here is the general syntax:

main.m
roots(polyVec)
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where polyVec is a vector containing the coefficients of the polynomial in decreasing order. For example,

main.m
p = [3 4 0 -1];
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represents the polynomial 3x^3 + 4x^2 - 1.

To find the roots of this polynomial, we can use the roots() function as follows:

main.m
r = roots(p)
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The result would be:

main.m
r =

    0.6438
   -1.0000
   -0.6438
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These values represent the roots of the polynomial.

Another function that can be used to find the roots of a polynomial is polyval(). This function evaluates the polynomial for a given input and can be used to confirm whether a particular value is a root of the polynomial.

Here is an example usage of polyval():

main.m
x = 1;
y = polyval(p, x)
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Output:

main.m
y =

     6
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Since the value of y is not zero, we can determine that x=1 is not a root of the polynomial.