How to solve a quadratic equation in python using numpy ?

Examples of how to solve a quadratic degree equation in python using numpy:

Example 1

With python we can find the roots of a polynomial equation of degree 2 ($ ax ^ 2 + bx + c $) using the function numpy: roots.

Consider for example the following polynomial equation of degree 2 $ x ^ 2 + 3x-0 $ with the coefficients $ a = 1 $, $ b = 3 $ and $ c = -4 $, we then find:

>>> import numpy as np
>>> coeff = [1,3,-4]
>>> np.roots(coeff)
array([-4.,  1.])

this equation has 2 real roots: $ x = -4 $ and $ x = 1 $.

Example 2

Another example with $x^2+3x=0$

>>> coeff = [1,3,3]
>>> np.roots(coeff)
array([-1.5+0.8660254j, -1.5-0.8660254j])

which admits only two complex roots: $x=-1.5+0.8660254j$ et $x=-1.5-0.8660254j$.

Example 3

Another example with $x^2-6x+9$

>>> coeff = [1,-6,9]
>>> np.roots(coeff)
array([ 3. +3.72529030e-08j,  3. -3.72529030e-08j])

which admits a real root here: $x=3$ (car $3.72529030e-08$ est proche de $0$)

References