Question

If the inequality $\sqrt{\frac{-3}{x^2+2x+10}}\ge 0$ holds good, then $x\in$

• A. $[0,\infty )$
• B. $(-\infty ,0]$
• C. $\varphi$
• D. $[2,14]$

Answer 1

The correct option is C $\varphi$

Given $\sqrt{\frac{-3}{x^2+2x+10}}\ge 0$ to be true
if $\frac{-3}{x^2+2x+10}\ge 0$
$\Rightarrow \frac{3}{x^2+2x+10}\le 0\Rightarrow x^2+2x+10<0\Rightarrow (x+1{)}^2+9<0$
which is not possible for any $x\in R$