(a(i))[3]
Determine the quotient when $x^4 - 2x^3 + 8x^2 - 12x + 13$ is divided by $x^2 + 6$ and confirm that the remainder is $1$.
(i)[3]
Determine the quotient when $x^4 - 2x^3 + 8x^2 - 12x + 13$ is divided by $x^2 + 6$ and confirm that the remainder is $1$.
(ii)[3]
Show that the equation $x^4 - 2x^3 + 8x^2 - 12x + 12 = 0$ has no real roots.