Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) 2/x=1+(x^3)

Question

I had a hard time finding the roots

Answer 1

After multiplying by x, the equation becomes x^4 + x -2 + 0

There are 2 real roots as you can see by the graph & the other 2 roots are complex.

You can see that 1 is a root by inspection and by using the Newton method, you get a second root of -1.353210

You cannot get the other 2 roots using Newtons method. So when you divide by x+1.353210, you end up with the quadratic equation x^2 -.35321x + 1.4779673

Use the quadratic equation to obtain the other 2 roots .176605 +- 1.20282i