Question

The number of negative values of $a$ for which the inequation $4^{x^2}+2(2a+1)2^{x^2}+{4a}^2-3>0$ is satisfied for any $x$ is

• A. $\infty$
• B. $0$
• C. $1$
• D. None of these

Answer 1

The correct option is A $\infty$

$4^{x^2}+2(2a+1)2^{x^2}+{4a}^2-3>0$
Put $2^{x^2}=t$
$t^2+2(2a+1)t+{4a}^2-3>0$
$\Rightarrow D<0$
$\Rightarrow 4(2a+1{)}^2-4(4a^2-3)<0$
$\Rightarrow a+1<0$
$\Rightarrow a<-1$
$\Rightarrow a\in (-\infty ,-1)$
Hence, infinite values of $a$ are possible.