Question

The range of $a$ for which $x^2-ax+1-2a^2$ is always positive for all real values of $x$, is

• A. $(-\frac{2}{3},\frac{2}{3}]$
• B. $[-\frac{2}{3},\frac{2}{3}]$
• C. $(-\frac{2}{3},\frac{2}{3})$
• D. $(-\infty ,1)$

Answer 1

The correct option is C $(-\frac{2}{3},\frac{2}{3})$

$x^2-ax+1-2a^2>0,\forall x\in R$
So,
$D<0\Rightarrow (-a{)}^2-4(1-2a^2)<0\Rightarrow 9a^2-4<0\Rightarrow a^2<\frac{4}{9}\therefore a\in (-\frac{2}{3},\frac{2}{3})$