Question

Use Newton’s method to find the real root (in four decimal places) near 0.5 of the equation x^5 −4x^2 + 2 = 0

Answer 1

Let f(x) is continuous function with be the initial approximation root of the f(x)=0 than the next root is given by .

In a simlar way the root is given by .

Given and by differentiating f(x) w.r.t x we get .

Now the

rearranging this

Putting we get ,

Similarly by putting in above expression we get the next iterations in the Netwon's merthod as

,

,

.

Hence the real root (in four decimal places) near 0.5 is 0.7471.