Show that it is impossible to find two real numbers with a product of 5 and a sum of 4.
Hint: think discriminants.
$\displaystyle xy = 5$
$\displaystyle x + y = 4$
$\displaystyle xy = 5 \rightarrow y = \frac{5}{x}$
$\displaystyle x + \frac{5}{x} = 4$ AND $\displaystyle x \neq 0$
$\displaystyle x^2 - 4x + 5 = 0$
Now find delta.
$\displaystyle b^2 - 4ac = 16 - 4(1)(5) = -4$
Therefore there exists only a complex solution.