Python Quadratic Equation

The quadratic equation has the form:ax²+bx+c=0。

Its solution can be found by evaluating the discriminant $\Delta = b^2 - 4ac$ to determine:

If $\Delta > 0$ , the equation has two real roots.
If $\Delta = 0$ , the equation has one real root (a double root).
If $\Delta < 0$ , the equation has no real roots, but has two complex roots.

The following example takes user input numbers and calculates the quadratic equation:

Example (Python 3.0+)

# Filename: quadratic_solver.py # Author: www.example.com (optimized by ChatGPT) # Program function: Solve the quadratic equation ax**2 + bx + c = 0 # Note: a ≠ 0, a, b, c are real numbers entered by the user import cmath # Import the cmath module to support complex number operations def get_float_input(prompt): """Get a floating-point number entered by the user, and handle invalid input. :param prompt: Prompt message :return: The floating-point number entered by the user""" while True: try: return float(input(prompt)) except ValueError: print("Please enter a valid number!") def solve_quadratic(a, b, c): """Calculate the solutions of the quadratic equation. :param a: Coefficient of the quadratic term :param b: Coefficient of the linear term :param c: Constant term :return: The two solutions of the quadratic equation""" discriminant = b**2 - 4*a*c # Calculate the discriminant root1 = (-b - cmath.sqrt(discriminant)) / (2 * a) root2 = (-b + cmath.sqrt(discriminant)) / (2 * a) return root1, root2 def main(): print("Solve the quadratic equation ax^2 + bx + c = 0") # Get user input a = get_float_input("Please enter the coefficient of the quadratic term a (a ≠ 0):") while a == 0: print("The coefficient a of the quadratic term cannot be 0!") a = get_float_input("Please re-enter the coefficient of the quadratic term a (a ≠ 0):") b = get_float_input("Please enter the coefficient of the linear term b:") c = get_float_input("Please enter the constant term c:") # Calculate and output the result root1, root2 = solve_quadratic(a, b, c) print(f"The solutions of the equation are: {root1} and {root2}") if __name__ == "__main__": main()

The output after running the above code is:

求解二次方程 ax^2 + bx + c = 0
请输入二次项系数 a（a ≠ 0）：1
请输入一次项系数 b：5
请输入常数项 c：6
方程的解为：(-3+0j) 和 (-2+0j)

In this example, we used the sqrt() method of the cmath (complex math) module to calculate the square root.

Example 2

import math
import cmath

def solve_quadratic(a, b, c):
"""
Solve the quadratic equation ax^2 + bx + c = 0
:param a: Coefficient of the quadratic term
:param b: Coefficient of the linear term
:param c: Constant term
:return: The solutions of the equation (may be real or complex)
"""
if a == 0:
# Handle non-quadratic equations
if b == 0:
return "No solution" if c != 0 else "The equation has infinitely many solutions"
return f"The equation is linear, and the solution is x = {-c / b}"

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

if delta > 0:
# Two real roots
root1 = (-b + math.sqrt(delta)) / (2 * a)
root2 = (-b - math.sqrt(delta)) / (2 * a)
return f"The equation has two real roots: x1 = {root1}, x2 = {root2}"
elif delta == 0:
# One real root
root = -b / (2 * a)
return f"The equation has a double real root: x = {root}"
else:
# Two complex roots
root1 = (-b + cmath.sqrt(delta)) / (2 * a)
root2 = (-b - cmath.sqrt(delta)) / (2 * a)
return f"The equation has two complex roots: x1 = {root1}, x2 = {root2}"

# Example call
a, b, c = 1, -3, 2
result = solve_quadratic(a, b, c)
print(result)

Document 对象参考手册 Python3 Examples

Other extensions

Python3Advanced Tutorial

Python Quadratic Equation

Example (Python 3.0+)

Example 2