**Write a Java program that prints all real and imaginary solutions to the quadratic equation **

**Week – 1**

** a)**** Aim: To Write a Java program that prints all real and **

**imaginary solutions to the quadratic equation ax**

^{2}+ bx +c = 0.**Read in a, b, c and use the quadratic formula.**

Description :

According to Linear Algebra of Quadratic Equations, The roots of a quadratic equation aX

^{2}+bX+c=0 depends on its discriminant values.The discriminant value d is calculated using the formula, d=b

^{2}-4aci. If d=0 then the roots are real and equal and the roots are -b/4a and –b/4a.

ii. 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

iii. If d<0 then the roots are imaginary.

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

**Source Code :**

import java.io.*;

import java.util.*;

class week2a

{

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(“nb = “);

b=s.nextInt();

System.out.print(“nc= “);

c=s.nextInt();

System.out.println(“The quadratic equation you entered is “+a+”x2+”+b+”x+”+c+”=0”);

System.out.print(“Its 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.

Please enter values

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

x

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

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