Question

If $f\left(x\right)=x^2-5x+6$ is a real-valued function, then

• A. $f\left(x\right)\ge 0$ when $x\in (-\infty ,2]\cup [3,\infty )$
• B. $f\left(x\right)\ge 0$ when $x\in [2,\infty )$
• C. $f\left(x\right)<0$ when $x\in (-\infty ,2)$
• D. $f\left(x\right)<0$ when $x\in (2,3)$

Answer 1

Answer: (A), (D)

$f\left(x\right)<0$ when $x\in (2,3)$

$f\left(x\right)=x^2-5x+6$
$=(x-2)(x-3)$


By wavy-curve method,
$f\left(x\right)\ge 0$ when $x\in (-\infty ,2]\cup [3,\infty )$
and $f\left(x\right)<0$ when $x\in (2,3)$