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4-2.Quadratic Equations and Inequations
hard
Let $\mathrm{S}$ be the set of positive integral values of $a$ for which $\frac{\mathrm{ax}^2+2(\mathrm{a}+1) \mathrm{x}+9 \mathrm{a}+4}{\mathrm{x}^2-8 \mathrm{x}+32}<0, \forall \mathrm{x} \in \mathbb{R}$. Then, the number of elements in $\mathrm{S}$ is :
A
$1$
B
$0$
C
$\infty$
D
$3$
(JEE MAIN-2024)
Solution
$ a x^2+2(a+1) x+9 a+4<0 \quad \forall x \in R $
$ \therefore a<0$
Standard 11
Mathematics
