Example 5.  Use the Newton-Horner's subroutine and the starting value to find a root of the polynomial
        .  
Run the Newton-Raphson subroutine and compare the two results (they should be close).

Solution 5.

Observe that the iterations are almost the same.  The reason they differ slightly is the method of evaluating the polynomial using powers of x verses nested multiplication.

(c) John H. Mathews 2004