• Introduction
• Solving quadratic equation using Python
• Complete code
• Conclusion

## Introduction

In algebra, quadratic equations are widely used in a lot of tasks. A quadratic equation (second-degree polynomial) always has a squared term which differentiates it from our usual linear equations.

In this tutorial we will use the math library (prebuilt in Python) for solving quadratic equations using Python.

We begin with understanding the standard form of quadratic equation:

$$ax^2 + bx + c = 0$$

where a, b, c are real numbers and $$a \neq 0$$.

So how do we know if the equation has a solution? And if it does, how many solutions?

#### Step 1: Calculating the discriminant

The first step to solve a quadratic equation is to calculate the discriminant. Using simple formula:

$$D = b^2 – 4ac$$

we can solve for discriminant and get some value. Next, if the value is:

• positive, then the equation has two solutions
• zero, then the equation has one repeated solution
• negative, then the equation has no solutions

#### Step 2: Solving for x values

To solve for each x value, we use the following quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} = \frac{-b \pm D}{2a}$$

which means that:

$$x_1 = \frac{-b + D}{2a}$$

$$x_2 = \frac{-b – D}{2a}$$

and these are all the steps we need to take to find the solution for the quadratic equation.

## Solving quadratic equation using Python

As an example, let’s consider the following quadratic equation:

$$x_1 – 5x_2 – 14 = 0$$

where $$a = 1$$, $$b = -5$$, and $$c = -14$$.

#### Step 1: Get user input for a, b, and c coefficients

First, we need to get these coefficients entered by the user:

a, b, c = eval(input("Please enter the a, b, c coefficients of your quadratic equation: "))


Here we will need to pass the three comma-separated values as: 1,-5,-14.

Clearly, if you pass anything other than a real number (string or boolean), it won’t break the input function but further calculations won’t work. To prevent this, you should consider adding a set of checks to validate the user input:

valid_input = True
while valid_input:
try:
float(a), float(b), float(c)
valid_input = False
except ValueError:
print("Please make sure the coefficients are real numbers and try again")
valid_input = True


So far we created the a, b, and c variables in Python.

#### Step 2: Calculate the discriminant

Next we will calculate discriminant. We will need to use the math library (prebuilt in Python) to use the square root function:

from math import sqrt

disc = sqrt(b*b-4*a*c)


For the values we entered above, the discriminant value should be 9.

#### Step 3: Find roots of the quadratic equation with quadratic formula using Python

And finally we solve for the roots of the equation. Recall that we also need to check if the discriminant is less than zero, then the quadratic equation has no solutions:

if disc >=0:
x1 = (-b+disc)/(2*a)
x2 = (-b-disc)/(2*a)
print("The roots of the equation are:", x1, x2)
else:
print("The equation has no solutions")


For our example we should get $$x_1 = 7$$ and $$x_2 = -2$$.

## Complete code

from math import sqrt

valid_input = True
while valid_input:
try:
float(a), float(b), float(c)
valid_input = False
except ValueError:
print("Please make sure the coefficients are real numbers and try again")
valid_input = True

disc = sqrt(b*b-4*a*c)

if disc >=0:
x1 = (-b+disc)/(2*a)
x2 = (-b-disc)/(2*a)
print("The roots of the equation are:", x1, x2)
else:
print("The equation has no solutions")


## Conclusion

In this article we covered how you can solve a quadratic equation using Python and math library.

Feel free to leave comments below if you have any questions or have suggestions for some edits and check out more of my Optimization articles.

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