Question

how to solve f(x) = 2x³+3x²-12x+1 

Answer 1

Step 1:

The cubic function is .

Solve the equation using Newton's approximation method.

Differentiate on each side with respect to .

Power rule of derivative is .

Newton's 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  .

Comments

Contd....

Step 5:

Now use the synthetic 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 .

Solution :

The roots of a cubic equation are and .