# Write a java program that prints all real and imaginary solutions to the quadratic equation

Contents

## Find the real and imaginary number of the complex number

In this program, we will learn to write a java program that prints all real and imaginary solutions to the quadratic equation ax2+ bx +c = 0. Read in a, b, c, and use the quadratic formula to find real and imaginary numbers calculator.

### Algorithm of Real and Imaginary Numbers

According to Linear Algebra of Quadratic Equations, The roots of a quadratic equation aX2+bX+c=0 depends on its discriminant values. The discriminant value is calculated using the formula, d=b2-4ac

• If d=0 then the roots are real and equal and the roots are  -b/4a and –b/4a.
• If d>0 then the roots are real and distinct and the roots are (-b+(b^2 –  4ac)^1/2) / 2a   and    (-b-(b^2 –  4ac)^1/2) / 2a
• If d < 0 then the roots are imaginary.

Based on these formulas, we are finding the roots of a quadratic equation.

### Source Code :

`import java.io.*;import java.util.*;class Imaginary{public static void main(String ar[]){int a,b,c,d;Scanner s=new Scanner(System.in);System.out.print("The Quadratic Equation is of the form ax2+bx+c=0. \n please enter values \na = ");a=s.nextInt();System.out.print("b = "+"\n");b=s.nextInt();System.out.print("c= "+"\n");c=s.nextInt();System.out.println("The quadratic equation you entered is "+a+"+x2+"+b+"+x+"+c+"=0");System.out.print("real and imaginary roots are");d=(b*b)-4*(a*c);if(d>0){System.out.println("Real and distinct");double rt1=(-b+Math.sqrt(d))/(2*a);double rt2=(-b-Math.sqrt(d))/(2*a);System.out.print("Roots are "+rt1 +" "+rt2);}else if(d==0){System.out.println("Real and equal");double rt1=(-b)/(2*a);double rt2=(-b)/(2*a);System.out.print("Roots are "+rt1 +" "+rt2);}else if(d<0){System.out.println("Imaginary");}}}`

### Expected output :

The Quadratic Equation is of the form ax2+bx+c=0.
a=1
b=2
c=1
The quadratic equation you entered is 1×2+2x+1=0
Its roots are Real and Equal
Roots are -1.0    -1.0