Find the least value of ‘a’ for which the function \( f(x) = x^2 + ax + 1 \) is increasing on the interval \( [1, 2] \).
If \( x, y, z \) are all different and
\[ \Delta = \begin{vmatrix} x^2 & x^3 + 1 \\ y^2 & y^3 + 1 \\ z^2 & z^3 + 1 \end{vmatrix} = 0, \text{ show that } xyz = -1. \]
