exception negative_arg of real;

  fun SQRT x = if x < 0.0
               then raise (negative_arg x)
               else sqrt x;

  fun quad_roots (a,b,c) =  (* assumes a is non-zero  *)
  let val discriminant = (b*b - 4.0*a*c)
      val d = SQRT discriminant
      val a2 = 2.0*a
  in  ([(~b + d)/a2,(~b - d)/a2],discriminant)
  end handle (negative_arg y) => ([],y);

val s1 = quad_roots (1.0,0.0,~1.0);   (*   X*X -1 ... has roots ~1 and 1 *)
val s2 = quad_roots (1.0,0.0,1.0);    (*   X*X +1 ... has no real roots. *)