(i)[4]
Determine the quotient and the remainder when $x^4 + x^3 + 3x^2 + 12x + 6$ is divided by $(x^2 - x + 4)$.
(ii)[2]
It is stated that, on dividing $x^4 + x^3 + 3x^2 + px + q$ by $(x^2 - x + 4)$, the remainder is zero. Determine the values of the constants $p$ and $q$.
(iii)[3]
With these values of $p$ and $q$, show that there is exactly one real value of $x$ that satisfies the equation $x^4 + x^3 + 3x^2 + px + q = 0$ and state that value.