Java Program to Find the Roots of Quadratic Equation
The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.
Conditions for a quadratic equation –
ax^2 + bx + c = 0 where a, b, c are real numbers and cannot be zero ie, there value must be from {-∞ to -1} and {1 to ∞}
A mathematical formula for finding the roots of a quadratic equation –
roots = (-b ± √(b2-4ac)) / (2a) ± represents there are two roots.
The roots of the quadratic equations are –
first = (-b + √(b2-4ac)) / (2a) second = (-b - √(b2-4ac)) / (2a)
The (b^2 – 4ac) which is the determinant, tells us about the nature of the roots –
- if (b^2 – 4ac) > 0, roots are real and different
- if (b^2 – 4ac) == 0, roots are real and equal
- if (b^2 – 4ac) < 0, roots are complex and different
Code to find roots of a quadratic equation:
// Java program to find the roots of
// quadratic equation
public class Main {
public static void main(String[] args)
{
// value of the constants a, b, c
double a = 7.2, b = 5, c = 9;
// declared the two roots
double firstroot, secondroot;
// determinant (b^2 - 4ac)
double det = b * b - 4 * a * c;
// check if determinant is greater than 0
if (det > 0) {
// two real and distinct roots
firstroot = (-b + Math.sqrt(det)) / (2 * a);
secondroot = (-b - Math.sqrt(det)) / (2 * a);
System.out.format(
"First Root = %.2f and Second Root = %.2f",
firstroot, secondroot);
}
// check if determinant is equal to 0
else if (det == 0) {
// two real and equal roots
// determinant is equal to 0
// so -b + 0 == -b
firstroot = secondroot = -b / (2 * a);
System.out.format(
"First Root = Second Root = %.2f;",
firstroot);
}
// if determinant is less than zero
else {
// roots are complex number and distinct
double real = -b / (2 * a);
double imaginary = Math.sqrt(-det) / (2 * a);
System.out.printf("First Root = %.2f+%.2fi",
real, imaginary);
System.out.printf("\nSecond Root = %.2f-%.2fi",
real, imaginary);
}
}
}
Time Complexity: O(log(D)), where D is the discriminant of the given quadratic equation.
Auxiliary Space: O(1)
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