Finding roots of a polynomial using Python

Question

How to use python to find all the roots of a polynomial function? My code below works if all the coefficients a, b, c, d, e in the my_func function are removed, that is, if they are equal to 1. How could I edit the code so that a, b, c, d, e (the arguments in the polynomial_root function) are defined in the said function?

Code:

import numpy as np


def polynomial_root(a,b,c,d,e):
        p = np.poly1d([a,b,c,d,e])
        roots = p.roots
        return roots

def my_func(x):
  return a*x**4 + b*x**3 - c*x**2 + d*x - e

def print_format(x, f):
    for i in range(0,4):
        print("x={}\t\t f(x)={}\t\t".format(x[i],f(x[i])))
  

# Working with polynomials 8x**4 + 3x**3 - 2x**2 + 8x - 2

c = polynomial_root(8.,3.,-2.,8.,-2)

print("The solutions of f(x) = 8x**4 + 3x**3 - 2x**2 + 8x - 2 are:")
print_format(c, my_func)

Answer 1

in your implementation of my_func, there are two problems:

• you use a, b, c, d and e as if they were global variables, but anywhere else you pass those coefficients as parameters
• you change the sign of c and e, therefore evaluating a different polynomial

a fixed version of your code could look like this:

import numpy as np


def polynomial_root(coefficients):
        p = np.poly1d(coefficients)
        return p.roots


def evaluate_polynomial(coefficients, x):
  result = 0
  for c, power in enumerate(reversed(coefficients)):
    result += c * x**power
  return result


def print_format(x_values, coefficients, f):
    for x in x_values:
        print("x={}\t\t f(x)={}\t\t".format(x, f(coefficients, x)))
  

# Working with polynomials 8x**4 + 3x**3 - 2x**2 + 8x - 2

coefficients = [8.,3.,-2.,8.,-2]
roots = polynomial_root(coefficients)

print("The solutions of f(x) = {}x**4 + {}x**3 + {}x**2 + {}x + {} = 0 are:".format(coefficients))
print_format(roots, coefficients, evaluate_polynomial)