If ( {{x}^{2}}+4ax+2>0 ) for all values of ( x, ) then (a) l... | Mathematics | SolveeIt | Solveeit

Today, August 24

Question

If ${{x}^{2}}+4ax+2>0$ for all values of $x,$ then $a$ lies in the interval

A

$(-2,\text{ }4)$

B

$(1, 2)$

C

$(-\sqrt{2},\sqrt{2})$

D

$\left( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$

Answer

$\left( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$

Explanation

Solution

${{x}^{2}}+4ax+2>0$
$\therefore$ ${{(4a)}^{2}}-4{{x}^{2}}<0$
[ $\because$ if $f(x)>0,$ then $D<0$ ]
$\Rightarrow$ $16{{a}^{2}}<8$
$\Rightarrow$ $ {{a}^{2}}