quadratic.py

## @package quadratic_solver
#This package contains a quadratic solver
import math


def quadratic_solver(a: float, b: float, c: float, complex_allowed: bool=False):
    '''Solves the quadratic equations in the form ax^2+bx+c=0, returning the roots as a list
    If complex roots are allowed, the returned values may be complex
    If complex roots are not allowed and there are no non-complex roots then a ValueError will be returned
    If both the quadratic and linear coefficients are zero then a ValueError will be returned
    Parameters:
    a (float): The quadratic coefficient
    b (float): The linear coefficient
    c (float): The constant
    complex_allowed (optional) (bool): If True, complex roots will be returned (if appropriate). If False, a ValueError will be returned if the discriminant is negative
    Returns:
    list(float): The root(s) of the equation. May be complex if complex_allowed is True and discriminant is negative'''
    if a == 0:
        if b == 0:
            ##If the quadratic and linear coefficients are both zero, raise a ValueError
            raise ValueError("Both 'a' and 'b' were zero, meaning there was no defined value for 'x'")
        else:
            ##If the quadratic coefficient is zero, return the constant divided by the linear coefficient
            return([-c / b])

    # Calculate the discriminant of the equation
    discriminant = b ** 2 - 4 * a * c

    if discriminant<0:
        if complex_allowed:
            ##If the discriminant is negative and complex roots are allowed, return two complex roots
           return([(-b-1j * math.sqrt(-discriminant))/(2 * a), (b+1j * math.sqrt(-discriminant))/(2 * a)])
        else:
            ##If the discriminant is negative and complex roots are not allowed, raise a ValueError
            raise ValueError("The discriminant was negative and complex results were not allowed")
    elif discriminant==0:
        ##If the discriminant is zero, return one real root
        return([-b / (2 * a)])
    else:
        ##If the discriminant is positive, return two real roots
        return([(-b -math.sqrt(discriminant)) / (2 * a), (-b + math.sqrt(discriminant)) / (2 * a)])