;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname oct12-dist-part1) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
(require "student-extras.rkt")

(define (root a b c)
  (/ (+ (- b) (sqrt (- (* b b) (* 4 a c))))
     (* 2 a)))


;(check-expect (root 1 2 1) -1)
;(check-expect (root 2 5 3) -1)

; if ax^2 + bx + c = 0,   what is x?
; Use the quadratic formula!
;
;  x = (-b + sqrt(b^2 - 4ac)) / 2a    (we'll ignore the - branch of the +/-)


(define discriminant 999)
(define two 2)

(define (root2 a b c)
  (let* {[discriminant (- (* b b) (* 4 a c))]
         [numerator   (+ (- b) (sqrt discriminant))]
         [denominator (* two a)]
         }
    (/ numerator denominator)))

; In `let`, the scope of the new identifiers is the let's body-expression (only).
; In `let*`, the scope of the new identifiers is ALL FOLLOWING RIGHT-HAND-SIDES,
;                                                and the let's body-expression.
; let* is equivalent to nested-lets;
;   in fact, internally it is syntactic sugar for just that.
;
;  "syntactic sugar" -- a language feature(syntax) which internally
;  gets re-written as other existing syntax.



(check-expect (root2 1 2 1) -1)
(check-expect (root2 2 5 3) -1)