Question

Apply Newton’s method to find the root of the polynomial of x⁴-2x³ 8x²-8 using a calculator.

Answer 1

To apply Newton's method to find the root of the given polynomial, start with an initial guess, find the equation of the tangent line, determine the x-intercept of the tangent line, and repeat until the root is found.

Step-by-step explanation:

1. Start with an initial guess for the root of the polynomial. Let's say we start with x = 1.
2. Using Newton's method, find the equation of the tangent line to the polynomial at the point (x, f(x)). The equation of the tangent line is given by y = f'(x)(x - x) + f(x), where f'(x) is the derivative of the polynomial.
3. Find the x-intercept of the tangent line, which will be our new guess for the root. We can do this by setting y = 0 and solving for x.
4. Repeat steps 2 and 3 until we reach a desired level of accuracy or until the root is found.
5. Using a calculator, perform the necessary calculations for each step. Start with x = 1 and continue until the root is found.