;Kitty

;First, we're going to be using the discriminant a lot, so let's code a function to calculate that. Leave out
;the sqrt, because discriminant means just the (b^2)-4ac underneath the root.

(define disc (lambda (a b c)
    (- (* b b)(* 4 a c))))

;We want a function that tells us about the roots. There are three possibilities:
;0 roots, 1 root, 2 rational roots, 2 irrational roots. That means we need three cases in our conditional.

;(define rootsOfQuadratic (lambda (a b c)
;    (cond (() "No real roots")
;          (() "One root")
;          (() "Two roots"))

;There's our four cases, so now we fill in the conditions that make them true.

(define rootsOfQuadratic (lambda (a b c)
    (cond ((< (disc a b c) 0) "No real roots")
          ((= (disc a b c) 0) "One root")
          ((> (disc a b c) 0) "Two roots"))))

;The second part is to extend the function to determine whether or not, in the case of two roots,
;if the roots are rational or not. To do this, we branch out the cond statement.

;(define rootsOfQuadratic2 (lambda (a b c)
;    (cond ((< (disc a b c) 0) "No real roots")
;          ((= (disc a b c) 0) "One root")
;          ((> (disc a b c) 0) (cond (() "Two rational roots")
;                                    (() "Two irrational roots"))))))

;And now we fill in the conditions.

(define rootsOfQuadratic2 (lambda (a b c)
    (cond ((< (disc a b c) 0) "No real roots")
          ((= (disc a b c) 0) "One root")
          ((> (disc a b c) 0) (cond ((Integer? (disc a b c)) "Two rational roots")
                                    ((Integer? (disc a b c)) "Two irrational roots"))))))

;That's a hell of a lot of parenthesis.