Question

To find a root of a polynomial equation, we can use an iterative process.
We start with an initial guess for the value of the root, x 0 , plug it in to the iterative formula and
solve for x 1 . Then we plug x 1 back into the iterative formula and solve for x 2 . We continue this
process until x n+1 and x n are equal to a specified number of decimal places. When this happens,
this is our approximate solution to the polynomial equation.
We will be solving for a root of a cubic equation:
f(x n ) = c3 x n 3 + c2 x n 2 + c1 x n + c0
where c3, c2, c1 and c0 are the coefficients of each polynomial term.
The iterative formula we will use is:
x n+1 = x n - ( f(x n ) / f '(x n ) )
where f '(x n )is the derivative of f(x n )

Define a public static method named cubicRoot that accepts the coefficients of the cubic
equation and an initial guess for the root . This method computes and returns a root of the cubic
equation by using the iterative process described below (you must use a while loop):
1. Start with the guess for the root passed to the method as x n

2. Compute x n+1 using the formula above Note: you can write the equation for the
derivative in terms of the coefficients, exponents and x terms.
3. Compare x n+1 and x n
i. if these are equal within 4 decimal places, then return the value
ii. If not, x n should be updated - repeat Step 2

in java code

Answer 1

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