The number of distinct real roots of $${x^4} - 4{x^3} + 12{x^2} + x - 1 = 0$$

The smallest value of $$k$$, for which both the roots of the equation $$${x^2} - 8kx + 16\left( {{k^2} - k + 1} \right) = 0$$$ are real, distinct and have values at least 4, is