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b) The Fibonacci sequence is defined by the following rule:

The fist two values in the sequence are 1 and 1. Every subsequent value is the sum of the two values preceding it. Write a Java program that uses both recursive and non recursive functions to print the nth value in the Fibonacci sequence.

import java.lang.*;

/**
*fibonacci**/
class Fibonacci
{
	public int nthfiborec(int n)
	{
	if (n==1||n=0)
		return 1;
	else
		return (nthfiborec(n-2)+nthfiborec(n-1));
	}

	public int nthfibo(int no)
	{
	int fib=0,num1=1,num2=1;

	for(int counter = 1; counter <= no-2; counter++)
	{
	fib=(num1 + num2);
	num1=num2;
	num2=fib;
	}
	return fib;
	}
}

class Mfibonacci
{
public static void main(String args[])
	{
	Fibonacci f=new Fibonacci();
	BufferedReader Br=new BufferedReader( new InputStreamReader(System.in));
System.out.print("Enter a number:");
	int n=Integer.pareseInt(br.readLine());
	System.out.println("The"+n+"th term of fibonacci series is "+f.nthfibo(n));
	System.out.println("The"+n+"th term of fibonacci series using recursion is "nthfibo(n-1));
	}
	System.out.println("k="+k);
}

a) Write a Java program that prints all real solutions to the quadratic equation ax2 + bx + c = 0. Read in a, b, c and use the quadratic formula. If the discriminant b2 -4ac is negative, display a message stating that there are no real solutions.

import java.lang.*;
import java.io.*;

/**
*	This class is used to determine the nature of quadratic equation  ( ax^2+bx+c=0 )
*   This Class requires java.lang and java.io</> packages to work
*	@author Shivu for www.btechadda.com
*/

class Quadratic
{
	private int CofA,CofB,CofC,Desc;//discriminant
	private double Root1,Root2;

	/**
	*	This discriminant is calcculated with the help of co-efficients CofA,CofB,CofC and then if its value is positive then roots are real and distinct
	* 	if desc is equla to 0 then roots are real and equal else if the roots are -ve then  roots are imaginary.
	*	CofA,CofB,Cofc shoud be read ...
	*	The values have read or not is checked by means CofDefined
	*
	*/
	public void calculate()
	{
		Desc=CofB*CofB-(4*CofA*CofC);
		if (Desc==0)
			{
			System.out.println("The roots are real and Equal");
			Root1=Root2=-CofB/(2*CofA);
			System.out.println("The roots are"+Root1+" and "+Root2);
			}
		else if(Desc>0)
			{
			System.out.println("The roots are real and distinct");
			Root1=((-CofB+Math.sqrt(Desc))/(2*CofA));
			Root2=((-CofB-Math.sqrt(Desc))/(2*CofA));
			System.out.println("The roots are"+Root1+" and "+Root2);

			}
		else
			{
			System.out.println("The roots are Imaginary");

			}

	}

	/**
	*	This method prompts the user for providing the input from the keyboard
	*	This method uses Buffered reader class, so it throws and IO exception , exception should be specified in public static void main
	*	This requires importing the java.io.BufferedReader , .InputSteamReader, Integer
	**/

	public void read() throws IOException
	{
	BufferedReader buffer=new BufferedReader(new InputStreamReader(System.in));
	System.out.print("Enter Co-efficient a:");
	CofA=Integer.parseInt(buffer.readLine());

	System.out.print("Enter Co-efficient b:");
	CofB=Integer.parseInt(buffer.readLine());

	System.out.print("Enter Co-efficient c:");
	CofC=Integer.parseInt(buffer.readLine());

	CofDefined=true;
	}
}

class Mquad
{
	public static void main(String[] argsf) throws IOException
	{
	Quadratic q1=new Quadratic();
	Quadratic q2=new Quadratic();
	q1.read();
	q1.nature();
	q2.nature();
	}
}