A class which will calculate the real roots of a polynomial, when given the coefficients.

Polynomial.java

import java.util.*;

public class Polynomial
{
    private static final double ROOT_LEEWAY = 0.000000001;
    private double[] coefficients;
    private double remainder;
    public Polynomial(double[] coefficients, double remainder)
    {
        this.coefficients = coefficients;
        this.remainder = remainder;
    }
    
    public Polynomial(double[] coefficients)
    {
        this.coefficients = coefficients;
        this.remainder = 0;
    }
    
    public ArrayList<Double> possibleRoots()
    {
        ArrayList<Double> possibilities = new ArrayList<Double>();
        double p = coefficients[coefficients.length - 1];
        double q = coefficients[0];
        
        ArrayList<Double> pFactors = findFactors(p);
        ArrayList<Double> qFactors = findFactors(q);
        
        for (Double pFactor : pFactors)
            for (Double qFactor : qFactors)
            {
                double possibility = pFactor / qFactor;
                if (!possibilities.contains(possibility))
            		possibilities.add(possibility);
            }
            
        return possibilities;
    }
    
    public ArrayList<Double> realRoots()
    {
        ArrayList<Double> roots = new ArrayList<Double>();
        ArrayList<Double> possibleRoots = possibleRoots();
        
        for (Double possibleRoot : possibleRoots)
        {
            double pluggedIn = plugin(possibleRoot);
        	if (Math.abs(pluggedIn) <= ROOT_LEEWAY)
        		roots.add(possibleRoot);
        }
        		
       	return roots;
    }
    
    public double plugin(double x)
    {
        double answer = 0;
        for (int i = 0; i < coefficients.length; i++)
            answer += coefficients[i] * Math.pow(x, coefficients.length - (i + 1));
        return answer;
    }
    
    public Polynomial divide(double divisor)
    {
        double[] newCoefficients = new double[coefficients.length - 1];
        newCoefficients[0] = coefficients[0];
        
        for (int i = 1; i < newCoefficients.length; i++)
            newCoefficients[i] = (newCoefficients[i - 1] * divisor) + coefficients[i];
        
        double remainder = (newCoefficients[newCoefficients.length - 1] * divisor) + coefficients[coefficients.length - 1];
        return new Polynomial(newCoefficients, remainder);
    }
    
    public double getRemainder()
    {
        return remainder;
    }
    
    public double[] getCoefficients()
    {
        return coefficients;
    }
    
    private ArrayList<Double> findFactors(double num)
    {
        ArrayList<Double> factors = new ArrayList<Double>();
        for (int i = (int)(-num); i <= num; i++)
        	if (num / i == (int)(num / i))
        		factors.add((double)i);
        		
        return factors;
    }
}