Here given a quadratic equation the task is to solve the equation or find out the roots of the equation. The standard form of a quadratic equation is –
ax2 + bx + c where, a, b, and c are coefficient and real numbers and also a ≠ 0. If a is equal to 0 that equation is not valid quadratic equation.
Examples Of Quadratic Equation:
Input :a = 1, b = 2, c = 1 Output : Roots are real and same -1.0 Input :a = 2, b = 2, c = 1 Output : Roots are complex -0.5 + i 2.0 -0.5 - i 2.0 Input :a = 1, b = 10, c = -24 Output : Roots are real and different 2.0 -12.0
Method 1: Using the direct formula
So here we describes different cases of Quadratic Equation:
If b*b < 4*a*c, then roots are complex (not real). For example roots of x2 + x + 1, roots are -0.5 + i1.73205 and -0.5 - i1.73205 If b*b == 4*a*c, then roots are real and both roots are same. For example, roots of x2 - 2x + 1 are 1 and 1 If b*b > 4*a*c, then roots are real and different. For example, roots of x2 - 7x - 12 are 3 and 4
Below program illustrate the quadratic equation in Python:
# Python program to find roots of quadratic equation import math # function for finding roots def equationroots( a, b, c): # calculating discriminant using formula dis = b * b - 4 * a * c sqrt_val = math.sqrt(abs(dis)) # checking condition for discriminant if dis > 0: print(" real and different roots ") print((-b + sqrt_val)/(2 * a)) print((-b - sqrt_val)/(2 * a)) elif dis == 0: print(" real and same roots") print(-b / (2 * a)) # when discriminant is less than 0 else: print("Complex Roots") print(- b / (2 * a), " + i", sqrt_val) print(- b / (2 * a), " - i", sqrt_val) # Driver Program a = 1 b = 10 c = -24 # If a is 0, then incorrect equation if a == 0: print("Input correct quadratic equation") else: equationroots(a, b, c)
real and different roots 2.0 -12.0
Method-2: Using Complex Math Module
# import complex math module import cmath a = 1 b = 4 c = 2 # calculating the discriminant dis = (b**2) - (4 * a*c) # find two results ans1 = (-b-cmath.sqrt(dis))/(2 * a) ans2 = (-b + cmath.sqrt(dis))/(2 * a) # printing the results print('The roots are') print(ans1) print(ans2)
The roots are (-3.414213562373095+0j) (-0.5857864376269049+0j)
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