% This program calculates the roots of the quadratic ax^2 + bx + c ==0
% INPUT COEFFICIENTS
disp(' This m-file calculates the roots of ')
disp('     a*x^2 + b*x + c = 0 ')
a = input(' Give a value for the leading coefficient ');
b = input(' Give a value for b ');
c = input(' Give a value for c ');

% Check if a is zero, if it is zero, we do not have a quadratic, but a
% linear equation
disp('  ');
if a==0
    disp(' a=0 :: Equation is linear in x');
    disp('  ');
    
    if (b==0 & c==0) % Additional checks on the remaining coefficients
        disp (' equation is undetermined '); % 0 * x = 0 has solutions all possible values of x
    elseif (b==0 & c~=0)
        disp (' equation 0*x = constant has no solution ! ');  % 0 * x = k has no solutions for x
    else
        x = -c / b;
        t = ['The unique Solution of ', num2str(b), '*x + ', num2str(c), ' = 0 is ', num2str(x)];
        disp(t);
        
    end
    
    % The else refers to what happens if the statement a==0 is false, i.e.
    % what happens if a is not zero (then we can solve for the two roots).
    
else
    d = b^2 - 4*a*c;  % Generate the discriminant and check to see if +ve or -ve
    
    if d >= 0 
        disp(' Two real roots ');
        x1 = (-b + sqrt(d))/(2*a)
        x2 = (-b - sqrt(d))/(2*a)
    else
        disp(' Two complex roots ');
        x1 = (-b + i*sqrt(-d))/(2*a)
        x2 = (-b - i*sqrt(-d))/(2*a)
    end
end