(i) To find \(a\) and \(b\), perform polynomial division of \(4x^4 + ax^2 + 11x + b\) by \(x^2 - x + 2\). The division gives a partial quotient of \(4x^2 + kx\).

Obtain the quotient \(4x^2 + 4x + a - 4\) or \(4x^2 + 4x + b/2\).

Equate the \(x\) or constant term to zero and solve for \(a\) or \(b\).

From the mark scheme, \(a = 1\) and \(b = -6\).

(ii) Show that \(x^2 - x + 2 = 0\) has no real roots.

Obtain roots \(\frac{1}{2}\) and \(-\frac{3}{2}\) from \(4x^2 + 4x - 3 = 0\).