Quadratic equations are used in calculating areas, calculating a product’s profit, or estimating an object’s speed. A quadratic equation is a second-degree equation. The standard form of the quadratic equation in python is written as px² + qx + r = 0. The coefficients in the above equation are p, q, r.
How do you do the Quadratic Equation in Python
The quadratic equation is written as (-b ± (b ** 2 – 4 * a * c) ** 0.5) / 2 * a. The standard form of the quadratic equation is given as ax^2+bx+c=0, a, b and c are real numbers and a ≠ 0
How do you find the Roots of Quadratic Equation in Python
When finding quadratic equation in python, one must consider the points discussed below:
The roots of a quadratic equation can be classified as:
- If b*b < 4*a*c, then roots are complex
- If b*b == 4*a*c, then roots are real, and both roots are the same.
- If b*b > 4*a*c, then roots are real and different
For example:
Input : p= 1, q= 2, r= 1
Output :
Roots are real and same
-1.0
Input : x = 2, y = 2, z = 1
Output :
Roots are complex
-0.5 + i 2.0
-0.5 – i 2.0
Input : x = 1, y = 10, z = -24
Output :
Roots are real and different
2.0
-12.0
Source Code:
#The following program is used to find out the roots of the quadratic equation
import math
def equationroots( x, y, z):
discri = y * y - 4 * x * z
sqrtval = math.sqrt(abs(discri))
# checking condition for discriminant
if discri > 0:
print(" real and different roots ")
print((-y + sqrtval)/(2 * x))
print((-y - sqrtval)/(2 * x))
elif discri == 0:
print(" real and same roots")
print(-y / (2 * x))
# when discriminant is less than 0
else:
print("Complex Roots")
print(- y / (2 * x), " + i", sqrt_val)
print(- y / (2 * x), " - i", sqrt_val)
# Driver Program
x = 1
y = 10
z = -24
if x == 0:
print("Input correct quadratic equation")
else:
equationroots(x, y, z)
Output:
real and different roots
2.0
-12.0
How do you write a Python Program to Solve Quadratic Equation
The program given below generates the quadratic equation when the a, b, c coefficients are known.
import c math
x = 1
y = 5
z = 6
# calculate the discriminant
w = (y**2) - (4*x*z)
# find two solutions
sol1 = (-y-cmath.sqrt(w))/(2*x)
sol2 = (-y+cmath.sqrt(w))/(2*x)
print('The solution are {0} and {1}'.format(sol1,sol2))
Output:
Enter x: 1
Enter y: 5
Enter z: 6
The solutions are (-3+0j) and (-2+0j)
What is the quadratic function formula?
The standard formula of a quadratic equation in Python is ax^2+bx+c=0.
In the above equation, a,b,c are the coefficients and real numbers and, a is not equal to zero. If a=0, then it will not be a valid quadratic equation.
The discriminant of the quadratic formula equation can be written as b^2-4ac
discriminant(d) = b² – 4*a*c
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