Question

The value of $a$ for which $-3<\frac{x^2+ax-2}{x^2+x+1}<2\forall x\in R$

• A. $(-2,1)$
• B. $(1,2)$
• C. $(0,3)$
• D. $(1,7)$

Answer 1

Answer: (A)

$(-2,1)$

Given, $-3<\frac{x^2+ax-2}{x^2+x+1}<2$
$\Rightarrow 0<4x^2+(a+3)x+1$ and $0<x^2+(2-a)x+4$
$D<0$ and $D<0$
$(a+3{)}^2-4\times 4<0$ and $(2-a{)}^2-4\times 4<0$
$-7$ Taking intersection, we get
$a\in (-2,1)$