Question

Find the values of $a$ for which $-3<\frac{x^2+ax-2}{x^2+x+1}<2$ is valid for all real $x$.

• A. $-2<a<1$
• B. $-4<a<2$
• C. $-2<a<2$
• D. $-4<a<0$

Answer 1

Answer: (A)

$-2<a<1$

$4x^2+(a+3)x+1>0$
$\Delta >0$
$(a+3{)}^2-16>0$
$a^2+6a-7>0$
$(a+7)(a-1)>0$
$aϵR-(-7,1)$
$-x^2+(a-2)x-4<0$
$\Delta <0$
$(a-2{)}^2-16<0$
$a^2-4a-12<0$
$(a-6)(a+2)<0$
$-2<a<6$
$aϵ(1,6)$