Please help- discriminants?

**greghunter** · November 2nd 2008, 07:36 AM

Show that it is impossible to find two real numbers with a product of 5 and a sum of 4.

Hint: think discriminants.

**janvdl** · November 2nd 2008, 07:55 AM

Originally Posted by greghunter

Show that it is impossible to find two real numbers with a product of 5 and a sum of 4.

Hint: think discriminants.

$xy = 5$
$x + y = 4$

$xy = 5 \rightarrow y = \frac{5}{x}$

$x + \frac{5}{x} = 4$ AND $x \neq 0$

$x^2 - 4x + 5 = 0$

Now find delta.

$b^2 - 4ac = 16 - 4(1)(5) = -4$

Therefore there exists only a complex solution.

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