# How do you solve x^2-6x+9<0 using a sign chart?

Feb 2, 2017

The solution is $S = \left\{\emptyset\right\}$

#### Explanation:

Let's factorise the LHS

${x}^{2} - 6 x + 9 = \left(x - 3\right) \left(x - 3\right) = {\left(x - 3\right)}^{2}$

Let $f \left(x\right) = {\left(x - 3\right)}^{2}$

${x}^{2} - 6 x + 9 < 0$

This is impossible since

$\forall x \in \mathbb{R} , f \left(x\right) > 0$