// bisection algorithm and f(x)
// hussein suleman
// 29 march 2004

public class Bisection
{
	static final double Epsilon = 0.000000001;
	
    // f(x) = x^7 + 6x^6 - 3x^5 + 4x^2 - x - 6
	public double f ( double x )
	{
		return (   Math.pow (x, 7)
		         + 6*Math.pow (x, 6)
		         - 3*Math.pow (x, 5)
		         + 4*Math.pow (x, 2)
		         - x
		         - 6 );
	}
	
    // find the root using a bisection algorithm
	public double findRoot ( double left, double right )
	{
		// calculate the midpoint
		double middle = (left+right) / 2;
				
		// iterate while the value is not close to 0
		while (Math.abs (f(middle)) > Epsilon)
		{
			System.out.println ("left = "+left+"   right = "+right);
			
			// halve interval
			if (f(left)*f(middle) < 0)
			   right = middle;
		    else
		       left = middle; 
		    
		    // calculate new midpoint
		    middle = (left+right) / 2;
		}
		return middle;
	}	
}