F.4 Quad. equation

(1) kx^2 - 4(x + k) = 1
kx^2 - 4x - (4k + 1) = 0
Let the roots be a and a - 4
Sum of roots = 2a - 4 = 4/k ... (1)
Product of roots a(a - 4) = -(4k + 1)/k ... (2)
(1) => a = 2/k + 2 ... (3)
Sub (3) into (2),
(2/k + 2)(2/k - 2) = -(4k + 1)/k
4/k^2 - 4 = -4 - 1/k
4/k^2 + 1/k = 0
(1/k)((4/k + 1) = 0
k = -4
(2) 3kx^2 + (2k + 3)x = x + k
3kx^2 + (2k + 2)x - k = 0
One root is negative of the other => Sum of roots = 0
-(2k + 2) / 3k = 0 => k = -1
-3x^2 + 1 = 0
x = +/-√3/3