Quadratic equations are defined as ax2 + bx + c = 0 where a, b, c are Real Numbers(or Complex Numbers) and x is a variable.
In High School for solving quadratic equations a formula is taught to kids,which is (-b±√(b²-4ac))/(2a) where different values(a, b, c) are taken from Quadratic equation. Mostly value of b²-4ac is referred to as Determinant of Quadratic Equation. So it can be said that formula for finding roots of a Quadratic Equation is (-b±√(d))/(2a). Do not that for roots to exist determinant value(d) should either be zero or 1.
Quite simple, let’s program this Mathematical Logic as Python Code for Solving Quadratic Equations.
# Finding roots of Quadratic Equation using Python # Import Python's Math Module import math a = float(input("Enter coefficient of x square =>")) b = float(input("Enter coefficient of x =>")) c = float(input("Enter constant value in equation =>")) # Calculating Determinant of Quadratic Equation d = b**2 - 4*a*c # Checking if Determinant is positive/zero if (d >= 0): # Calculating Roots of Quadratic Equation first_root = (-b + math.sqrt(d))/2*a second_root = (-b - math.sqrt(d))/2*a print("Roots of Quadratic Equation are =>", first_root,",", second_root) else: print("Roots don't exist")
Output of Above Code
Enter coefficient of x square =>1 Enter coefficient of x =>-4 Enter constant value in equation =>3 Roots of Quadratic Equation are => 3.0 , 1.0