answer the question with haskell code

Exercise 2. Suppose we have the following in a script. Perform equational reasoning by hand execution for the function roots. Use a = 1, b = 2, c = 1, and then check with the computer:

f::Double -> Double -> Double -> Bool

f a b c = if (b^2-4*a*c) < 0 then False else True

g::Double -> Double -> Double -> Double

g a b c = (b^2-4*a*c)

roots::Double -> Double -> Double -> Maybe (Double, Double)

roots a b c

| f a b c == False = Nothing

| otherwise =

let r = sqrt(g a b c)

x1 = (-b + r)/2*a

x2 = (-b - r)/2*a