Question

i need help

5. (10 points) Definition of Algorithm: Use the discussion in Section 3.3 of our textbook to find all integral roots (if any exist) of the following polynomial. Hint: Consider writing a short program. In: f(z) = 6r3 +42-1z +2

Answer 1

Code:

import java.util.Scanner;

public class Main
{
public static void main(String args[]) throws Exception
{
int x=0,y,pos_roots=0,neg_roots=0;
y=(6*x*x*x)+(4*x*x)-(7*x)+2;
for(x=0;x<1000000;x++)//checks for positive integeral roots
{
if(y==0)
{
System.out.println(x+" is a root of the equation 6x^3+4x^2-7x+2=0");
pos_roots++;
}
}

System.out.println("There are total "+pos_roots+" positive roots for the equation 6x^3+4x^2-7x+2=0");

for(x=0;x>-1000000;x--)//checks for negative integeral roots
{
if(y==0)
{
System.out.println(x+" is a root of the equation 6x^3+4x^2-7x+2=0");
neg_roots++;
}
}

System.out.println("There are total "+neg_roots+" negative roots for the equation 6x^3+4x^2-7x+2=0");
}
}
Output:

sample [CUsers'darshiDesktopyHomeworkLibsample] - srcMain.java [sample] Intelliu IDEA Eie Edit צ¡ew Navigate gode Analyze Befactor Build Run lools VCs window Help *- @Main.java × sampl import javauLil.Scanner 3 public class Main public static void main(String args) throws Exception Exte int x-0,y,pos roots-,neg_roots0; Scratch8 for (x-0;x160000e;x++)//checks for positive integeral roots 18 12 System.out.println(x+" is a root of the equation 6xA3+4xA2-7x+2-0"); pos_rools++; 14 15 16 17 18 System.out.println("There are total "+pos roots+" positive roots for the equation 6xA3+4x 2-7x+2-") 28 for (xx-1000eeex)//checks for negative integerol roots 23 24 Svstem.out.println(xt is a root of the eauation 6xA3+4xA2-7x+2-0") Main main Run: Main "C:\Program There are total θ positive roots for the equation 6x^3+4x^2-7x+2-e There are total negative roots for th equation 6xA3+4xA2-7x+2-0 ↑ Files\Java\jdk-10.อ.2(bin\java .exe" "-javaagent:C:\Program Files\JetBrains\Inteli î] IDEA Community Edition 2018.2(lib\idea-rt.jar=5501{ 4: Run ,:-TODO -Terminal Messages Event Lag Compilation completed successfully in 1 s 691 ms (a minute ago) Type here to search 0421 27-03-2019