NCERT Computer Science Class #11 – Chapter #7 Solutions – Q #10

Chapter #7 – Functions

Chapter #7 – Lab Exercises #3

Write a program that has a user defined function to accept the coefficients of a quadratic equation in variables and calculates its determinant. For example : if the coefficients are stored in the variables a,b,c then calculate determinant as b²-4ac. Write the appropriate condition to check determinants on positive, zero and negative and output appropriate result.

def calculate_determinant(a, b, c):
    """Calculate the determinant of a quadratic equation."""
    return b**2 - 4*a*c

def main():
    # Accepting coefficients from the user
    try:
        a = float(input("Enter the coefficient a: "))
        b = float(input("Enter the coefficient b: "))
        c = float(input("Enter the coefficient c: "))
        
        # Ensure 'a' is not zero for a valid quadratic equation
        if a == 0:
            print("Coefficient 'a' cannot be zero for a quadratic equation.")
            return
        
        # Calculate the determinant
        determinant = calculate_determinant(a, b, c)
        
        # Check the value of the determinant and output the result
        if determinant > 0:
            print("The determinant is positive. The quadratic equation has two distinct real roots.")
        elif determinant == 0:
            print("The determinant is zero. The quadratic equation has exactly one real root (repeated).")
        else:
            print("The determinant is negative. The quadratic equation has no real roots (two complex roots).")
    
    except ValueError:
        print("Invalid input. Please enter numeric values for coefficients.")

# Run the main function
if __name__ == "__main__":
    main()

You can checkout the code from Github here – Lab Exercises #3

Explanation of the Code:

1.    Function Definition:
      •	calculate_determinant(a, b, c): This function calculates the determinant 
        using the formula b2−4ac.

2.    Main Function:
      •	Prompts the user to input the coefficients a, b, and c.
      •	Checks if aa is zero (since it would not be a quadratic equation).
      •	Calls calculate_determinant to compute the determinant.
      •	Evaluates the value of the determinant and prints messages based on whether 
        it is positive, zero, or negative.

Example 1: Positive Determinant:

Input:

Enter the coefficient a: 1
Enter the coefficient b: 5
Enter the coefficient c: 6

Output:

The determinant is positive. The quadratic equation has two distinct real roots.

Explanation: 

The determinant calculated is 52 – 4 × 1 × 6 = 25 – 24 = 1 which is positive.

Example 2: Zero Determinant

Input:

Enter the coefficient a: 1
Enter the coefficient b: 4
Enter the coefficient c: 4

Output:

The determinant is zero. The quadratic equation has exactly one real root (repeated).

Explanation:

The determinant calculated is 42 – 4 × 1 × 4 = 16 – 16 = 0  which is zero.

Example 3: Negative Determinant

Input:

Enter the coefficient a: 1
Enter the coefficient b: 2
Enter the coefficient c: 5

Output:

The determinant is negative. The quadratic equation has no real roots (two complex roots).

Explanation:

The determinant calculated is 22 – 4 × 1 × 5 = 4 – 20 = −16  which is negative.

NCERT Computer Science Class 11 Chapter 7 Solutions Q 10