Question

Solve: $x^2-5x+6\ge 0$

• A. $[-\infty ,2)\cup [3,\infty )$
• B. $[-\infty ,4)\cup [3,\infty )$
• C. $[-\infty ,2)\cup [7,\infty )$
• D. None of these

Answer 1

The correct option is A $[-\infty ,2)\cup [3,\infty )$

R.E.F image

$x^2-5x+6\ge 0$

$\Rightarrow (x-2)(x-3)\ge 0$

$x<2(x-2)(x-3)>0$

$\Rightarrow x\in (-\infty ,2)\cup (3,\infty )$

($\because (x-2)(x-3)$ has odd power $\therefore$ sign change at $2,3$)