Question

(Algebra: solve quadratic equations)

The two roots of a quadratic equation, for example, , can be obtained using the following formula:

r1 = (-b + sqrt(b^2 - 4ac) / (2a) and r1 = (-b - sqrt(b^2 - 4ac) / (2a)

b^2 - 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots.

Write a program that prompts the user to enter values for a, b, and c and displays the result based on the discriminant.

If the discriminant is positive, display two roots.

If the discriminant is 0, display one root.

Otherwise, display “The equation has no real roots”.

Sample Run 1

Enter a: 1.0

Enter b: 3

Enter c: 1

The roots are -0.3819660112501051 and -2.618033988749895

Sample Run 2

Enter a: 1

Enter b: 2.0

Enter c: 1

The root is -1.0

Sample Run 3

Enter a: 1

Enter b: 2

Enter c: 3

The equation has no real roots.

In python.

Answer 1

#code.py
a = eval(input("Enter a: "))
b = eval(input("Enter b: "))
c = eval(input("Enter c: "))
d = b * b - 4.0 * a * c
if (d < 0):
    print("The equation has no real roots.")
elif (d == 0):
    root1 = -b / (2.0 * a)
    print("The root is",root1)
elif (d > 0 ):
    root1 =(-b + d**0.5) / (2.0 * a)
    root2 =(-b - d**0.5) / (2.0 * a)
    print("The roots are",root1,"and",root2)

Enter a: 1.0
Enter b: 3
Enter c: 1
The roots are -0.3819660112501051 and -2.618033988749895