Question

 Use Newton’s method to approximate the indicated root of the equation correct to six decimal places.

The root of  x^4 - 2 x^3 + 5 x^2 - 6 = 0 in the interval [1, 2]

Answer 1

Step 1:

in the interval

Newton's approximation method formula :  .

Step 2:

Step 3:

Step 4:

Step 5:

Since and are agree to six decimal places, then the root of equation .

Solution :

The root of the equation .