Question

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Answer 1

Answer:

In this program, you'll learn to find all roots of a quadratic equation and print them using format() in Java.

To understand this example, you should have the knowledge of the following Java programming topics:

Java if...else Statement

Java Math sqrt()

The standard form of a quadratic 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)

root1 = (-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 real and equal

if determinant < 0, roots are complex complex and different

Example: Java Program to Find Roots of a Quadratic Equation

public class Main {

public static void main(String[] args) {

// value a, b, and c

double a = 2.3, b = 4, c = 5.6;

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

In the above program, the coefficients a, b, and c are set to 2.3, 4, and 5.6 respectively. Then, the determinant is calculated as b2 - 4ac.

Based on the value of the determinant, the roots are calculated as given in the formula above. Notice we've used library function Math.sqrt() to calculate the square root of a number.

We have used the format() method to print the calculated roots.

The format() function can also be replaced by printf() as:

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

Answer 2

is not the answer understood