10.
$$\mathrm { f } ( x ) = x ^ { 2 } + 4 k x + ( 3 + 11 k ) , \quad \text { where } k \text { is a constant. }$$
- Express \(\mathrm { f } ( x )\) in the form \(( x + p ) ^ { 2 } + q\), where \(p\) and \(q\) are constants to be found in terms of \(k\).
Given that the equation \(\mathrm { f } ( x ) = 0\) has no real roots,
- find the set of possible values of \(k\).
Given that \(k = 1\),
- sketch the graph of \(y = \mathrm { f } ( x )\), showing the coordinates of any point at which the graph crosses a coordinate axis.