Question

$f\left(x\right)=\frac{2x^2-5x+7}{(x-1)(x-2)(x-3)}$ is continuous or not?

Answer 1

$2x^2-5x+7=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{5\pm \sqrt{25-4\left(2\right)\left(7\right)}}{4}$

$x=\frac{5\pm \sqrt{-31}}{4}$

Hence $2x^2-5x+7=0$ does not have roots as 1,2,3.

Hence f(x) is continuous for all x.