$\"\"$

The function is $\"\"$ .

Rewrite the above function.

$\"\"$ .

Consider $\"\"$ .

Graph:

Graph of function $\"\"$ .

$\"\"$

Observe the graph :

The function touches $\"\"$ -axis at $\"\"$ and $\"\"$ .

Roots of the function $\"\"$ are $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Newtons approximation method formula : $\"\"$ .

Consider one root as $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table :

The root of the equation is $\"\"$ .

$\"\"$

Consider root as $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table :

The root of the equation is $\"\"$ .

$\"\"$

The roots of the function $\"\"$ is $\"\"$ and $\"\"$ .