Java program to find all roots of a quadratic equation
Write a java program to find all roots of a quadratic equation
The standard form of an equation is:
ax2+bx+c=0
Here, a, b and c are real numbers and a can't be equal to 0.
We can calculate the root of a quadratic by using the formula
x=−b±b2−4ac−−−−−−−√2a
The ± sign indicates that there will be two roots:
root1=−b +b2−4ac−−−−−−−√2a
root2=−b -b2−4ac−−−−−−−√2a
The term b2-4ac is known as the determinant of a quadratic equation. It specifies the nature of roots. That is,
- if determinant > 0, roots are real and different
- if determinant < 0, roots are complex and different
- if determinant == 0, roots are real and equal
- Program:
public class Main {
public static void main(String[] args) {
// value a, b, and c
double a = 4.6, b = 2, c = 4.2;
double root1, root2;
// calculate the determinant (b2 - 4ac)
double determinant = b * b - 4 * a * c;
// check if determinant is greater than 0
if (determinant > 0) {
// two real and distinct roots
root1 = (-b + Math.sqrt(determinant)) / (2 * a);
root2 = (-b - Math.sqrt(determinant)) / (2 * a);
System.out.format("root1 = %.2f and root2 = %.2f", root1, root2);
}
// check if determinant is equal to 0
else if (determinant == 0) {
// two real and equal roots
// determinant is equal to 0
// so -b + 0 == -b
root1 = root2 = -b / (2 * a);
System.out.format("root1 = root2 = %.2f;", root1);
}
// if determinant is less than zero
else {
// roots are complex number and distinct
double real = -b / (2 * a);
double imaginary = Math.sqrt(-determinant) / (2 * a);
System.out.format("root1 = %.2f+%.2fi", real, imaginary);
System.out.format("\nroot2 = %.2f-%.2fi", real, imaginary);
}
}
}- Output:
root1 = -0.22+0.93i root2 = -0.22-0.93i
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