Problem source

Consider the equation
\[
x^2 - b x + c = 0 \;,
\]
where  $b$ and $c$ are real numbers.
\begin{questionparts}
\item Show that the roots of the equation
are  real and positive if and only if $b>0$ and \phantom{} $b^2\ge4c>0$, and sketch the region of the 
$b\,$-$c$ plane in which these conditions hold.
\item  Sketch the region of 
the $b\,$-$c$ plane in which the roots of the equation are real and less
than $1$ in magnitude.
\end{questionparts}