The equation \(x^3 - 30x^2 + 108x - 104 = 0\) has

no real roots;

exactly one real root;

three distinct real roots;

a repeated root.

Let \(f(x) = x^3 - 30x^2 + 108x - 104\).

By searching for small integer solutions, we find that \[f(2) = 8 - 120 + 216 - 104 = 0,\] so \((x - 2)\) is a factor of \(f(x)\). Then we can factorise completely to find \[f(x) = (x - 2)(x^2 - 28x + 52) = (x - 2)(x - 2)(x - 26),\] so \(f(x)\) has a repeated root and the answer is (d).