Find the roots of the polynomials using NumPy

• Difficulty Level : Hard
• Last Updated : 05 Sep, 2020

In this article, let’s discuss how to find the roots of a polynomial of a NumPy array. It can be found using various methods, let’s see them in detail.

Method 1: Using np.roots()

This function returns the roots of a polynomial with coefficients given in p. The coefficients of the polynomial are to be put in an array in the respective order.

For example, if the polynomial is x2 +3x + 1, then the array will be [1, 3, 1]

Syntax : numpy.roots(p)

Parameters :
p : [array_like] Rank-1 array of polynomial coefficients.

Return : [ndarray] An array containing the roots of the polynomial.

Let’s see some examples:

Example 1: Find the roots of polynomial x2 +2x + 1

Python3

 # import numpy libraryimport numpy as np    # Enter the coefficients of the poly in the arraycoeff = [1, 2, 1]print(np.roots(coeff))

Output:

[-1. -1.]

Example 2: Find the roots of the polynomial x3 +3 x2   + 2x +1

Python3

 # import numpy libraryimport numpy as np    # Enter the coefficients of the poly # in the arraycoeff = [1, 3, 2, 1]print(np.roots(coeff))

Output:

[-2.32471796+0.j         -0.33764102+0.56227951j -0.33764102-0.56227951j]

Method 2: Using np.poly1D()

This function helps to define a polynomial function. It makes it easy to apply “natural operations” on polynomials. The coefficients of the polynomial are to be put in an array in the respective order.

For example, for the polynomial x2 +3x + 1, the array will be [1, 3, 1]

Approach:

• Apply function np.poly1D() on the array and store it in a variable.
• Find the roots by multiplying the variable by roots or r(in-built keyword) and print the result to get the roots of the given polynomial

Syntax: numpy.poly1d(arr, root, var):

Let’s see some examples:

Example 1: Find the roots of polynomial x2 +2x + 1

Python3

 # import numpy libraryimport numpy as np    # enter the coefficients of poly # in the arrayp = np.poly1d([1, 2, 1])  # multiplying by r(or roots) to # get the rootsroot_of_poly = p.rprint(root_of_poly)

Output:

[-1. -1.]

Example 2: Find the roots of the polynomial x3 +3 x2   + 2x +1

Python3

 # import numpy libraryimport numpy as np    # enter the coefficients of poly# in the arrayp = np.poly1d([1, 3, 2, 1])  # multiplying by r(or roots) to get # the rootsroot_of_poly = p.rprint(root_of_poly)

Output:

[-2.32471796+0.j         -0.33764102+0.56227951j -0.33764102-0.56227951j]

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