polyroot#

Purpose#

Computes the roots of a polynomial given the coefficients.

Format#

y = polyroot(c)#

Parameters:

c ((N+1)x1 vector) –

coefficients of an Nth order polynomial:

\[p(z) = c[1]*z^n + c[2]*z^{n-1} + ... + c[n]*z + c[n+1]\]

Returns:

y (Nx1 vector) – the roots of c.

Examples#

/*
** Consider the polynomial
** y = 7x^4 - 5x^3 + 4x - 3
*/

/*
** First create vector of coefficients.
** Note that because there is no x^2 term
** we must place a 0 as the third element
*/
c = 7|(-5)|0|4|(-3);

// Find roots
roots = polyroot(c);

// Print roots
print "The roots of the polynomial y = 7x^4 - 5x^3 + 4x - 3 are:"
roots;

The output reads:

The roots of the polynomial y = 7x^4 - 5x^3 + 4x - 3 are:
     -0.83614991
      0.40754502 +       0.72864999i
      0.40754502 -       0.72864999i
      0.73534559

Remarks#

Zero leading terms will be stripped from c. When that occurs the order of y will be the order of the polynomial after the leading zeros have been stripped.

\(c[1]\) need not be normalized to unity.

Source#

poly.src