Java program to find all the roots of a quadratic equation

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In this program, you will learn to find all the roots of a quadratic equation and use Java's format() to print them.

The standard form of a quadratic equation is:

ax2　+　bx　+　c = 0, where
a, b and c are real numbers,
a ≠ 0

The b²-4ac is called the determinant of the quadratic equation. The determinant explains the nature of the roots.

• If the determinant is greater than 0, then the roots are real and different.

• If the determinant is equal to 0, then the roots are real and equal.

• If the determinant is less than 0, then the roots are complex and different.

Example: Java program to find the roots of a quadratic equation

public class Quadratic {
　　　　public static void main(String[] args) {
　　　　　　　　double a =　2.3, b =　4, c =　5.6;
　　　　　　　　double root1, root2;
　　　　　　　　double determinant = b　*　b　-　4　*　a　*　c;
　　　　　　　　//The condition for real different roots
　　　　　　　　if(determinant > 0) {
　　　　　　　　　　　　root1　= (-b　+　Math.sqrt(determinant))　/　(2　*　a);
　　　　　　　　　　　　root2　= (-b　-　Math.sqrt(determinant))　/　(2　*　a);
　　　　　　　　　　　　System.out.format("root1　= %.2f and root2　= %.2f, root1　, root2);
　　　　　　　　}
　　　　　　　　//The condition for real equal roots
　　　　　　　　else if(determinant == 0) {
　　　　　　　　　　　　root1　= root2　=　-b　/　(2　*　a);
　　　　　　　　　　　　System.out.format("root1　= root2　= %.2f;", root1);
　　　　　　　　}
　　　　　　　　//If the root is not a real number
　　　　　　　　else {
　　　　　　　　　　　　double realPart =　-b　/　(2　*a);
　　　　　　　　　　　　double imaginaryPart = Math.sqrt(-determinant)　/　(2　*　a);
　　　　　　　　　　　　System.out.format("root1　= %.2f+%.2fi and root2　= %.2f-%.2fi", realPart, imaginaryPart, realPart, imaginaryPart);
　　　　　　　　}
　　　　}
}

When running the program, the output is:

root1　=　-0.87+1.30i and root2　=　-0.87-1.30i

In the above program, the coefficients a, b, and c are set to2.3,4and5.6. Then, calculate the determinant as b² - 4ac.

According to the value of the determinant, calculate the root as shown in the formula. Note that we have already used the library functionMath.sqrt()to calculate the square root of a number.

Use the format() function in Java to print the calculated root (real root or complex root) on the screen. The format() function can also be replaced with printf():

System.out.printf("root1　= root2　= %.2f;", root1);

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