diff --git a/cyclotomic.cabal b/cyclotomic.cabal
--- a/cyclotomic.cabal
+++ b/cyclotomic.cabal
@@ -1,5 +1,5 @@
 Name:                cyclotomic
-Version:             0.4.2
+Version:             0.4.3
 Synopsis:            A subfield of the complex numbers for exact calculation.
 Description:         The cyclotomic numbers are a subset of the
                      complex numbers that are represented exactly, enabling exact
@@ -22,7 +22,7 @@
 Tested-with:         GHC == 7.6.3
 Library
   Exposed-modules:     Data.Complex.Cyclotomic
-  Build-depends:       base >= 4.2 && < 4.7,
+  Build-depends:       base >= 4.2 && < 4.8,
                        containers >= 0.3 && < 0.6,
                        arithmoi >= 0.4 && < 0.5
   Hs-source-dirs:      src
diff --git a/src/Data/Complex/Cyclotomic.hs b/src/Data/Complex/Cyclotomic.hs
--- a/src/Data/Complex/Cyclotomic.hs
+++ b/src/Data/Complex/Cyclotomic.hs
@@ -60,31 +60,32 @@
 -}
 
 module Data.Complex.Cyclotomic
-    (Cyclotomic
-    ,i
-    ,e
-    ,sqrtInteger
-    ,sqrtRat
-    ,sinDeg
-    ,cosDeg
-    ,sinRev
-    ,cosRev
-    ,gaussianRat
-    ,polarRat
-    ,polarRatDeg
-    ,polarRatRev
-    ,conj
-    ,real
-    ,imag
-    ,isReal
-    ,isRat
-    ,isGaussianRat
-    ,toComplex
-    ,toReal
-    ,toRat
-    ,goldenRatio
-    ,dft
-    ,dftInv
+    ( Cyclotomic
+    , i
+    , e
+    , sqrtInteger
+    , sqrtRat
+    , sinDeg
+    , cosDeg
+    , sinRev
+    , cosRev
+    , gaussianRat
+    , polarRat
+    , polarRatDeg
+    , polarRatRev
+    , conj
+    , real
+    , imag
+    , isReal
+    , isRat
+    , isGaussianRat
+    , toComplex
+    , toReal
+    , toRat
+    , goldenRatio
+    , dft
+    , dftInv
+    , rootsQuadEq
     )
     where
 
@@ -545,3 +546,18 @@
 dftInv cs = [minv * sum (zipWith (*) [e m^(k*n) | n <- [0..]] cs) | k <- [0..m-1]]
           where m = fromIntegral $ length cs
                 minv = fromRational (1 % m)
+
+-- | Solutions to the quadratic equation
+--   a x^2 + b x + c = 0.
+--   Returns 'Nothing' if a == 0.
+rootsQuadEq :: Rational  -- ^ a
+            -> Rational  -- ^ b
+            -> Rational  -- ^ c
+            -> Maybe (Cyclotomic,Cyclotomic)  -- ^ roots
+rootsQuadEq a b c
+    | a == 0     = Nothing
+    | otherwise  = Just ((-bb + sqrtDisc)/(2*aa),(-bb - sqrtDisc)/(2*aa))
+    where
+      aa = fromRational a
+      bb = fromRational b
+      sqrtDisc = sqrtRat (b*b - 4*a*c)
diff --git a/src/Tests.hs b/src/Tests.hs
--- a/src/Tests.hs
+++ b/src/Tests.hs
@@ -3,13 +3,34 @@
 module Main where
 
 import Data.Complex.Cyclotomic
-import Test.Framework (defaultMain, testGroup)
+import Test.Framework
+    ( defaultMain
+    , testGroup
+    )
 import Test.Framework.Providers.HUnit
+    ( testCase
+    )
 import Test.Framework.Providers.QuickCheck2
+    ( testProperty
+    )
 import qualified Test.Framework.Providers.SmallCheck as S
 import qualified Test.Framework.Providers.API as T
+import Test.QuickCheck
+    ( Gen
+    , elements
+    , Arbitrary(..)
+    , shrinkRealFrac
+    )
 import Test.HUnit
+    ( (@?=)
+    , Assertion
+    )
+import Data.List
+    ( nub
+    )
 import Data.Ratio
+    ( (%)
+    )
 
 main :: IO ()
 main = defaultMain tests
@@ -24,14 +45,15 @@
         ,qc_Gauss
         ,qc_dftInv_dft
         ,qc_dft_dftInv
+        ,qc_sum_quadratic_roots
         ]
 
 rationals :: [Rational]
 rationals = 0 % 1 : [sign * k % j | n <- [0..], m <- [0..n-1], sign <- [1,-1]
                     , let k = m + 1, let j = n - m, gcd k j == 1]
 
-cyclotomics :: [Cyclotomic]
-cyclotomics = 0 : undefined
+rationalList :: Integer -> [Rational]
+rationalList m = nub [n % d | n <- [-m..m], d <- [1..m]]
 
 test1a :: T.Test
 test1a = testGroup "polarRat" [polarRatTest p q | p <- [0..10], q <- [1..10]]
@@ -71,6 +93,26 @@
                          then (-1 + sqrtInteger nn) / 2
                          else (-1 + i*sqrtInteger nn) / 2
 
+prop_dftInv_dft :: [Rational] -> Bool
+prop_dftInv_dft rs = dftInv (dft cs) == cs
+    where cs = map fromRational rs
+
+prop_dft_dftInv :: [Rational] -> Bool
+prop_dft_dftInv rs = dft (dftInv cs) == cs
+    where cs = map fromRational rs
+
+prop_sum_quadratic_roots :: (Rational, Rational, Rational) -> Bool
+prop_sum_quadratic_roots (a, b, c)
+    = case rootsQuadEq a b c of
+        Nothing      -> a == 0
+        Just (r1,r2) -> r1 + r2 == fromRational (-b / a)
+
+prop_sum_quadratic_roots_small :: (SmallRational, SmallRational, SmallRational) -> Bool
+prop_sum_quadratic_roots_small (SmallRational a, SmallRational b, SmallRational c)
+    = case rootsQuadEq a b c of
+        Nothing      -> a == 0
+        Just (r1,r2) -> r1 + r2 == fromRational (-b / a)
+
 ----------------------
 -- QuickCheck Tests --
 ----------------------
@@ -99,10 +141,6 @@
                          })
       $ testProperty "QuickCheck prop_Gauss" prop_Gauss
 
-prop_dftInv_dft :: [Rational] -> Bool
-prop_dftInv_dft rs = dftInv (dft cs) == cs
-    where cs = map fromRational rs
-
 qc_dftInv_dft :: T.Test
 qc_dftInv_dft
     = T.plusTestOptions (T.TestOptions
@@ -115,10 +153,6 @@
                          })
       $ testProperty "QuickCheck prop_dftInv_dft" prop_dftInv_dft
 
-prop_dft_dftInv :: [Rational] -> Bool
-prop_dft_dftInv rs = dft (dftInv cs) == cs
-    where cs = map fromRational rs
-
 qc_dft_dftInv :: T.Test
 qc_dft_dftInv
     = T.plusTestOptions (T.TestOptions
@@ -130,4 +164,25 @@
                          ,T.topt_timeout                            = Nothing
                          })
       $ testProperty "QuickCheck prop_dft_dftInv" prop_dft_dftInv
+
+qc_sum_quadratic_roots :: T.Test
+qc_sum_quadratic_roots
+    = testProperty "QuickCheck prop_sum_quadratic_roots" prop_sum_quadratic_roots_small
+
+----------------------
+-- QuickCheck Stuff --
+----------------------
+
+data SmallRational = SmallRational Rational
+                     deriving (Show,Ord,Eq)
+
+smallRationalList :: [SmallRational]
+smallRationalList = map SmallRational (rationalList 3)
+
+smallRationalGen :: Gen SmallRational
+smallRationalGen = elements smallRationalList
+
+instance Arbitrary SmallRational where
+    arbitrary = smallRationalGen
+    shrink (SmallRational r) = map SmallRational (shrinkRealFrac r)