# Python | Finding Solutions of a Polynomial Equation

Given a quadratic equation, the task is to find the possible solutions to it.

Examples:

```Input :
enter the coef of x2 : 1
enter the coef of x  : 2
enter the costant    : 1
Output :
the value for x is -1.0

Input :
enter the coef of x2 : 2
enter the coef of x  : 3
enter the costant    : 2
Output :
x1 = -3+5.656854249492381i/4 and x2 = -3-5.656854249492381i/4
```

Algorithm :

```Start.
Prompt the values for a, b, c.
Compute i = b**2-4*a*c
If i get negative value g=square root(-i)
Else h = sqrt(i)
Compute e = -b+h/(2*a)
Compute f = -b-h/(2*a)
If condition e==f then
Print e
Else
Print e and f
If i is negative then
Print -b+g/(2*a) and -b-g/(2*a)
stop
```

Below is the Python implementation of the above mentioned task.

 `# Python program for solving a quadratic equation. ` `  `  `from` `math ``import` `sqrt    ` `try``:      ` ` `  `    ``# if user gives non int values it will go to except block ` `    ``a ``=` `1` `    ``b ``=` `2` `    ``c ``=` `1` `    ``i ``=` `b``*``*``2``-``4` `*` `a ``*` `c ` ` `  `    ``# magic condition for complex values ` `    ``g ``=` `sqrt(``-``i) ` `    ``try``: ` `        ``d ``=` `sqrt(i) ` `        ``# two resultants ` `        ``e ``=` `(``-``b ``+` `d) ``/` `2` `*` `a   ` `        ``f ``=` `(``-``b``-``d) ``/` `2` `*` `a ` `        ``if` `e ``=``=` `f: ` `            ``print``(``"the values for x is "` `+` `str``(e)) ` `        ``else``: ` `            ``print``(``"the value for x1 is "` `+` `str``(e) ``+` `                  ``" and x2 is "` `+` `str``(f)) ` `    ``except` `ValueError: ` `        ``print``(``"the result for your equation is in complex"``) ` `         `  `        ``# to print complex resultants. ` `        ``print``(``"x1 = "` `+` `str``(``-``b) ``+` `"+"` `+` `str``(g) ``+` `"i/"` `+` `str``(``2` `*` `a) ``+`  `              ``" and x2 = "` `+` `str``(``-``b) ``+` `"-"` `+` `str``(g) ``+` `"i/"` `+`  `              ``str``(``2` `*` `a))    ` `         `  `except` `ValueError: ` `    ``print``(``"enter a number not a string or char"``) `

Output :

`the values for x is -1.0`

Explanation :
First, this program will get three inputs from the user. The values are the coefficient of , coefficient of and constant. Then it performs the formula

For complex the value of gets negative. Rooting negative values will throw a value error. In this case, turn the result of and then root it. Don’t forget to include at last.

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