7.
$$\mathrm { f } ( x ) = x ^ { 2 } + ( k + 3 ) x + k$$
where \(k\) is a real constant.
- Find the discriminant of \(\mathrm { f } ( x )\) in terms of \(k\).
- Show that the discriminant of \(\mathrm { f } ( x )\) can be expressed in the form \(( k + a ) ^ { 2 } + b\), where \(a\) and \(b\) are integers to be found.
- Show that, for all values of \(k\), the equation \(\mathrm { f } ( x ) = 0\) has real roots.