Solving 2nd degree equations • Write the following Java methods • boolean real-s

Question

Solving 2nd degree equations

• Write the following Java methods

• boolean real-sols(double a, double b, double c): it returns true if the 2nd degree equation ax2 + bx + c has real solutions • double solution1(double a, double b, double c): If the equation ax2 + bx + c has real solutions it return the smallest of the two. If it doesn’t have real solutions it should return the value 0 and an error message.

• double solution2(double a, double b, double c): If the equation ax2 + bx + c has real solutions it return the biggest of the two. If it doesn’t have real solutions it should return the value 0 and an error message.

• Test your methods within a class and check that they work properly. Use the method real-sols(double a, double b, double c) in the implementation of the other 2 methods.

Explanation / Answer

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
class Ideone
{
   static boolean real_sols(double a, double b, double c){
       return (b*b)-(4*a*c)>=0;
   }
  
   static double solution1(double a, double b, double c){
       double det = (b*b)-(4*a*c);
       if(det<0){
           System.out.println("Roots are imaginary");
           return 0;
       }
       double s1 = (-b+Math.sqrt(det))/(2*a);
       double s2 = (-b-Math.sqrt(det))/(2*a);
       return Math.min(s1,s2);
   }
   static double solution2(double a, double b, double c){
       double det = b*b-4*a*c;
       if(det<0){
           System.out.println("Roots are imaginary");
           return 0;
       }
       double s1 = (-b+Math.sqrt(det))/(2*a);
       double s2 = (-b-Math.sqrt(det))/(2*a);
       return Math.max(s1,s2);
   }
   public static void main (String[] args) throws java.lang.Exception
   {
       double a, b, c;
       a = 1;
       b = 1;
       c = 1;
       System.out.println("Roots are real "+real_sols(a,b,c));
       a = 1;
       b = -3;
       c = 2;
       System.out.println("Roots are real "+real_sols(a,b,c));
       System.out.println("Smallest soln is "+solution1(a,b,c));
       System.out.println("Largest soln is "+solution2(a,b,c));
   }
}

Output:

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