How do you solve x^2+3>2x using a sign chart?

Feb 27, 2017

The solution is $x \in \mathbb{R}$

Explanation:

Let's rewrite the equation

${x}^{2} - 2 x + 3 > 0$

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

We need the roots of

${x}^{2} - 2 x + 3 = 0$

Let's calculate the discriminant

$\Delta = {b}^{2} - 4 a c = {\left(- 2\right)}^{2} - 4 \left(3\right) \left(1\right)$

$= 4 - 12 = - 8$

As, $\Delta < 0$, there are no real roots

So,

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

graph{x^2-2x+3 [-6.176, 6.31, -0.31, 5.93]}