Use Newton's method to estimate the requested solution of the equation. Start with given value of x0 and then give x2 as
the estimated solution.
-$$x ^ { 3 } + 5 x + 2 = 0 ; x _ { 0 } = - 1 ; \text { Find the one real solution. }$$
A) -0.39
B) -0.64
C) -0.44
D) -0.38

Question

Quizplus · Accepted Answer

The Newton-Raphson formula is given by:

$$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$

where $f(x)=x^3+5x+2$ is the given function.

Using the formula, we have:

$$x_1=x_0-\frac{f(x_0)}{f'(x_0)}$$
$$= -1- \frac{(-4)}{(3(-1)^2+5)}$$
$$= -0.4667$$

Thus, we have $x_1= -0.4667$.

Now,

$$x_2=x_1-\frac{f(x_1)}{f'(x_1)}$$
$$= -0.4667-\frac{(0.1114)}{12.44}$$
$$= -0.4444$$

Therefore, the estimated solution is $x_2= -0.4444$ which is closest to option C = -0.44.

Use Newton's Method to Estimate the Requested Solution of the Equation