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Python Programs - Conditional Statements

Find roots of a quadratic equation (real/imaginary) - Python Program

Example 1 :

Python 
import math

a = float(input("a: "))
b = float(input("b: "))
c = float(input("c: "))

d = b**2 - 4*a*c

if d > 0:
    root1 = (-b + math.sqrt(d)) / (2*a)
    root2 = (-b - math.sqrt(d)) / (2*a)
    print("Real roots:", root1, root2)
elif d == 0:
    root = -b / (2*a)
    print("Equal roots:", root)
else:
    real = -b / (2*a)
    imag = math.sqrt(-d) / (2*a)
    print("Imaginary roots:", f"{real}+{imag}i", f"{real}-{imag}i")

Output

 
OUTPUT 1 :
a: 5
b: 4
c: 2
Imaginary roots: -0.4+0.4898979485566356i -0.4-0.4898979485566356i

OUTPUT 2 :
a: 1
b: 2
c: 1
Equal roots: -1.0 

OUTPUT 3 :
a: 1
b: -5
c: 2
Real roots: 4.561552812808831 0.4384471871911697

Example 2 : Advanced Program

Python 
import cmath

def find_quadratic_roots(a, b, c):
    """
    Calculates the roots of a quadratic equation ax^2 + bx + c = 0.

    Args:
        a (float): Coefficient of x^2.
        b (float): Coefficient of x.
        c (float): Constant term.

    Returns:
        tuple: A tuple containing the two roots (real or complex).
               If 'a' is 0, it indicates an invalid quadratic equation.
    """
    if a == 0:
        return "Error: 'a' cannot be zero for a quadratic equation."

    discriminant = (b**2) - 4 * a * c

    if discriminant >= 0:
        # Real roots
        root1 = (-b + cmath.sqrt(discriminant)) / (2 * a)
        root2 = (-b - cmath.sqrt(discriminant)) / (2 * a)
        return root1, root2
    else:
        # Complex (imaginary) roots
        root1 = (-b + cmath.sqrt(discriminant)) / (2 * a)
        root2 = (-b - cmath.sqrt(discriminant)) / (2 * a)
        return root1, root2

# Get input from the user
try:
    a = float(input("Enter coefficient 'a': "))
    b = float(input("Enter coefficient 'b': "))
    c = float(input("Enter coefficient 'c': "))

    roots = find_quadratic_roots(a, b, c)

    if isinstance(roots, str):
        print(roots)  # Print error message if 'a' is 0
    elif roots[0] == roots[1]:
        print(f"The quadratic equation has one real root (repeated): {roots[0]:.4f}")
    elif isinstance(roots[0], complex):
        print(f"The quadratic equation has two complex roots: {roots[0]:.4f} and {roots[1]:.4f}")
    else:
        print(f"The quadratic equation has two distinct real roots: {roots[0]:.4f} and {roots[1]:.4f}")

except ValueError:
    print("Invalid input. Please enter numeric values for coefficients.")

Output

 
OUTPUT 1 :
Enter coefficient 'a': 1
Enter coefficient 'b': -5
Enter coefficient 'c': 6
The quadratic equation has two complex roots: 3.0000+0.0000j and 2.0000+0.0000j

OUTPUT 2 :
Enter coefficient 'a': 1
Enter coefficient 'b': 2
Enter coefficient 'c': 1
The quadratic equation has one real root (repeated): (-1.0000+0.0000j)

OUTPUT 3 :
Enter coefficient 'a': 1
Enter coefficient 'b': 2
Enter coefficient 'c': 5
The quadratic equation has two complex roots: (-1.0000+2.0000j) and (-1.0000-2.0000j)

Explanation

Import cmath:

The cmath module is imported to handle complex number calculations, specifically for finding the square root of negative numbers, which occurs when the roots are imaginary.

find_quadratic_roots Function:

  • Takes three arguments: a, b, and c, representing the coefficients of the quadratic equation ax^2 + bx + c = 0.
  • Handles a = 0: Checks if ais zero. If it is, the equation is not a quadratic equation, and an error message is returned.
  • Calculates Discriminant:The discriminant (b^2 - 4ac) is calculated. This value determines the nature of the roots.
  • Real Roots (Discriminant >= 0):If the discriminant is non-negative, the roots are real. The standard quadratic formula is applied, and sqrt() is used for consistency, although math.sqrt() would also work for non-negative values.
  • Complex Roots (Discriminant < 0):If the discriminant is negative, the roots are complex (imaginary). sqrt() is essential here as it can handle the square root of negative numbers, returning a complex number.
  • Returns a tuple containing the two calculated roots.

User Input and Output:

 

  • Prompts the user to enter the values for coefficients a, b, and c.
  • Calls the find_quadratic_rootsfunction to get the roots.

 

Conditional Output:

  • If the function returns an error string (due to a=0), it prints the error.
  • If the two roots are equal, it indicates a single, repeated real root.
  • If the roots are complex (checked using isinstance(roots[0], complex)), it prints them as complex numbers.
  • Otherwise, it prints the two distinct real roots.
  • Includes a try-exceptblock to handle ValueError if the user enters non-numeric input.

 

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