Finding Polynomial Constant k Based on Roots

Consider the function defined by the polynomial equation:

$$ f(x) = 3x^4 - 8x^3 + 6x^2 - 12x + k $$

where $k$ is a constant. The function intersects the x-axis at four points, namely $x = -2$, $x = 1$, $x = 2$, and $x = p$. If the polynomial has a double root at $x = 1$, what is the value of $k$?