python program to find roots of the quadratic equation

certainly! a quadratic equation is a second-degree polynomial equation of the form:

\[ ax^2 + bx + c = 0 \]

where \( a \), \( b \), and \( c \) are coefficients, and \( x \) represents the unknown variable. the roots of the quadratic equation can be found using the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

### steps to find the roots of a quadratic equation

1. **understand the coefficients**: identify the values of \( a \), \( b \), and \( c \).
2. **calculate the discriminant**: the discriminant \( d \) is given by \( d = b^2 - 4ac \). it helps determine the nature of the roots:
- if \( d 0 \): two distinct real roots.
- if \( d = 0 \): one real root (a repeated root).
- if \( d 0 \): no real roots (two complex roots).
3. **calculate the roots**: use the quadratic formula to find the roots based on the value of \( d \).

### python code example

here's a python program that implements the above steps to find the roots of a quadratic equation:

### how to use the code:

1. **input the coefficients**: when you run the program, it will prompt you to enter the coefficients \( a \), \( b \), and \( c \).
2. **check for validity**: the program checks that \( a \) is not zero, as this would not constitute a quadratic equation.
3. **output the roots**: the program calculates and prints the roots, which could be real or complex.

### additional notes:

- the `cmath` module is used because it can handle square roots of negative numbers, returning complex roots when necessary.
- this program assumes that the user will input valid numerical values. for production code, you may want to add error handling to manage invalid inputs.

### example run:

in this example, the quadratic equation \( x^2 - 3x + 2 = 0 \) has roots at \( x = 2 \) and \( x = 1 \). the output shows these roots in the form of complex numbers, where the imaginary part is zero (indicating real roots).

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