Let \[\mathrm{S}\] be the set of positive integral values of a
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Official solution
x2−8x+32>0∀x∈R as discriminant of this quadratic is 64−4×32<0
\[
\Rightarrow a x^2+2(a+1) x+9 a+4<0 \forall x \in R
\]
⇒ Only possible when a<0 and D<0⇒ Since S is set of positive
values of a⇒S is a null set
\[
\Rightarrow n(S)=0
\]