Question

Identify all of the real roots of x^3-5x^2+8x+4=0.

Answer 1

To find the real roots of such this complex polynomials there are so many methods are available.

One of the methods to find the real root is Newton Raphson method.

According to Newton Raphson method, approximate values of real roots are determine using formula

, where n = 1, 2, 3, .....

Finding iteration continued upto

When  and when

Let the approximate root is zero

Now,

Here the first approximation is

Now ,

Here the second approximation is

Now ,

Here the third approximation is

Now ,

Here the fourth approximation is

Now ,

The real root of the equation is .