Answer: \(k\le-25\) or \(k\ge-1\).

Answer: \(k\le-25\) or \(k\ge-1\).

For the equation to have real roots, the discriminant must be non-negative:

\(b^2-4ac\ge0\).

Here \(a=k\), \(b=k+5\) and \(c=-4\). Therefore

\((k+5)^2-4(k)(-4)\ge0\).

Expanding gives

\(k^2+10k+25+16k\ge0\),

so

\(k^2+26k+25\ge0\).

Factorising,

\((k+1)(k+25)\ge0\).

The product is non-negative outside the two roots \(-25\) and \(-1\). Hence

\(k\le-25\quad\text{or}\quad k\ge-1\).