Step 1: \ \

The cubic equation is .

Solve the equation using Newtons approximation method.

Differentiate on each side with respect to .

Power rule of derivative is .

Newtons approximation method formula :  .

Step 2: \ \

Consider .

Step 3: \ \

Repeat the step 2 with .

Step 4: \ \

Repeat the step 2 with .

So one root of the equation is  .

Step 5: \ \

Now use the synthatic division method to find the remaining roots.

The function is .

Perform the synthetic substitution method with .

So the cubic equation can be written as .

Now solve the quadratic equation :

Formula for the root of a quadratic equation is .

Therefore the roots of a cubic equation are and .