Let S be the set of positive integral values | vedclass

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(B) Given the inequality $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}  0$ for all $x \

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$0$

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(B) Given the inequality $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32} Since the denominator $x^2-8x+32 = (x-4)^2 + 16 > 0$ for all $x \in R$,the inequality holds if and only if the numerator $f(x) = ax^2+2(a+1)x+9a+4 For $f(x) However,the question asks for the set $S$ of positive integral values of $a$.Since $a$ must be negative for the inequality to hold for all $x$,there are no positive integral values of $a$ that satisfy the condition.Therefore,the set $S$ is empty,and the number of elements in $S$ is $0$.

Let $S$ be the set of positive integral values of $a$ for which $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32} < 0, \forall x \in R$. Then,the number of elements in $S$ is:

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