Use Newton's method to find all roots of the equation correct to six decimal places? Square root (x+1)=x^2-x
Let us define a function
and find its derivative with respsct to x
from above expression we conclude that if x=-1 ,then f'(x) is not defined.
The Newton method is
`x_(k+1)=x_k-f(x_k)/(f'(x_k))` , prvided `f'(x_k)!=0` for any `x_k.`
Now draw the graph of f(x) to estimate the initial approximation
From graph we observe that roots of the given equation lies in (-1,0) and (1,2).
1. let approximation of first root be -.5 i.e `x_0=-.5`
Simlarly second root can be calculated which is near t the point x=2.