Question

For what real numbers x is x^2-6x+9 negative?

Answer 1

$x^2-6x+9=0$

1. For what numbers the function is null ?

$\Delta = b^2-4ac = 0$
$\Delta = 0$, so there is one solution :

$x = \frac{-b}{2a} = 3$

2. For what numbers the function is negative ?

The function is a parabola upturned ($a\ \textgreater \ 0$), so if its don't cut the abscissa line (0 to 1 solution where the function is null), there is no negative numbers.

Here, there is just one solution who cut the abscissa line, so there is no solution for the negative function.

The function is never negative.