Question

The values of $x$ for which $x^2\ge 4a$ holds true, is

• A. $[2\sqrt{a},\infty )$
• B. $(-\infty ,-2\sqrt{a}]\cup [2\sqrt{a},\infty )$
• C. $(-\infty ,-a)\cup [a,\infty )$
• D. $(-\infty ,-\sqrt{a}]\cup [\sqrt{a},\infty )$

Answer 1

The correct option is B $(-\infty ,-2\sqrt{a}]\cup [2\sqrt{a},\infty )$

$x^2\ge 4a\Rightarrow |x|\ge 2\sqrt{a}\Rightarrow x\ge 2\sqrt{a}\text{or}x\le -2\sqrt{a}\therefore x\in (-\infty ,-2\sqrt{a}]\cup [2\sqrt{a},\infty )$