Java Program to Find the Roots of a Quadratic Equation

This is the Java Program to Find the Roots of a Quadratic Equation.

Problem Description

Given the coefficients of the quadratic equation, write a Java Program to Find the roots of the quadratic equation.

Problem Solution

Calculate the determinant using the formula B² – 4*A*C, and then according to its value calculate the roots, whether they are real and unequal, real and equal, or imaginary.

Program/Source Code

Here is the source code of the Java Program to Find the Roots of a Quadratic Equation. The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.

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//Java Program to Find the Roots of a Quadratic Equation

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import java.io.BufferedReader;
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import java.io.InputStreamReader;
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public class Quadratic {
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    // Function to find and display the roots of the equation.

    public static void main(String[] args) {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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        double a,b,c;
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        try{
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            System.out.println("Enter the coefficients of the quadratic equation");

            a = Double.parseDouble(br.readLine());

            b = Double.parseDouble(br.readLine());

            c = Double.parseDouble(br.readLine());

```
        }catch (Exception e){
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            System.out.println("An error occurred");

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            return;
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        }
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        double determinant = Math.pow(b,2) - 4*a*c;

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        if(determinant > 0){
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            System.out.println("Roots are " + (-b+Math.sqrt(determinant))/(2*a)

                                  + " and " + (-b-Math.sqrt(determinant))/(2*a));

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        }else if (determinant == 0){
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            System.out.println("Roots are " + -b/(2*a));

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        }
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        else{
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            System.out.println("Roots are " + -b/(2*a) + "+i" +

                                Math.sqrt(-determinant)/(2*a) + " and "

                                + -b/(2*a) + "-i" + Math.sqrt(-determinant)/(2*a));

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        }
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    }
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}
```

Program Explanation

In the function main(), firstly the coefficients are entered in the variables a,b and c respectively. Then the determinant is calculated (double determinant = Math.pow(b,2) – 4*a*c;). Now, according to the value of the determinant, the roots are displayed using an if-else ladder.

Time Complexity: O(1).

Runtime Test Cases

 
Case 1 (Simple Test Case - Real and Unequal Roots):
 
Enter the coefficients of the quadratic equation
1
-5
6
Roots are 3.0 and 2.0
 
Case 2 (Simple Test Case - Real and Equal Roots):
 
Enter the coefficients of the quadratic equation
1
-2
1
Roots are 1.0
 
Case 3 (Simple Test Case - Imaginary roots):
 
Enter the coefficients of the quadratic equation
1
1
1
Roots are -0.5+i0.8660254037844386 and -0.5-i0.8660254037844386

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