# Create Program to Solve Polynomial in Racket in Racket Assignment Solution

July 08, 2024
Professor Benjamin
🇦🇺 Australia
Programming
Professor Mitchell is a renowned educator with over 20 years of experience teaching computer science at leading universities in the UK and Australia. He has completed over 600 Programming assignments and excels in teaching foundational concepts such as basic syntax, OOP principles, and functional programming in Groovy. Professor Mitchell's expertise lies in simplifying complex topics and fostering a deeper understanding of Groovy programming.
Key Topics
• Instructions
• Requirements and Specifications
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## Instructions

Objective

Write a racket assignment program to create a BST tree.

## Requirements and Specifications

Write a recursive function that finds a zero of a polynomial using the false position method.

The function takes 3 parameters: The polynomial function and two starting values.

Test this function with the two following polynomials:

For the function 9x2 - 3x - 25, you can use starting values 0 and 4:

Which evaluate to -25 and 107 respectively

You can assume that the two starting x values evaluate to y values that are on opposite sides of the x axis. (i.e. one y value is positive, the other negative)

For the function y = 11x2 - 2x – 50, you can use starting values -5 and 1:

Which evaluate to 235 and -41 respectively

Print out the final x value.

a subfunction to decide if the current y value is accurate enough. The accuracy can be hard coded (0.001 or 0.0001 or so) or can be a parameter.

a subfunction that calculates the x-intercept of a line segment given two endpoints.

Screenshots of output

Source Code

```#lang racket ;myPolynomial subfunction (define (myPolynomial x) (- (- (* 9 (* x x )) (* 3 x)) 25) ) ;myOtherPolynomial subfunction (define (myOtherPolynomial x) (- (- (* 11 (* x x )) (* 2 x)) 50) ) ;xIntercept subfunction (define (xIntercept a fa b fb) (/ (- (* a fb) (* b fa)) (- fb fa)) ) ; helper function to get the sign of the number: -1 = negative, 1 = positive, 0 = 0 (define (sign x) (cond [(> x 0) 1] [(< x 0) -1] [else 0] ) ) ;recursive function (define (root-iter f a b acc) (let* ([fa (f a)] [fb (f b)] [c (xIntercept a fa b fb)] [fc (f c)]) (cond [(< (abs fc) acc) c] [(= (sign fa) (sign fc)) (root-iter f c b acc)] [else (root-iter f a c acc)] ) ) ) (display "Root of myPolinomial: ") (root-iter myPolynomial 0. 4. 0.00001) (newline) (display "Root of myOtherPolinomial: ") (root-iter myOtherPolynomial -3.0 0.0 0.00001) (newline) ```

## Related Samples

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