Task $1$: Absolute Difference between roots of Quadratic equations $[30$ marks$]$

There are many kinds of equations to solve in algebra. One of the most common kind of equations are

quadratic equations, which come in the form of $a{x}^2+bx+c=0,$ where $x$ is the variable, and $a,b$ and $c$

are the coefficients of the equation. In $628AD,$ Brahmagupta explicitly described the general formula to be:

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

Assuming that $b^{2}4ac$ holds, the equation will have two real roots $($which might be equal$).$

You are given an incomplete code for a Python function rootAbsDiff $)$ that takes in the three

coefficients $a,b,$ and $c$ of a quadratic equation. You may assume that rootAbsDiff is always called with the

three coefficients such that $b^{2}4ac.$ Every time when it is called, rootAbsDiff calculates the two roots of

the equation and returns the absolute difference between the two roots.

You may use the sqrt function from the math library to help you calculate square roots. You might also

use the abs function $($which is a built$-$in function in Python to help you calculate absolute values.$)$

Complete the definition of rootAbsDiff, and test its correctness in Python shell, as follows:

$$ rootAbsDiff$(1,2,1)$

$0\mathrm{.}0$