Frobenius & Special Functions · Challenge problem

The equation $x^2y'' + 7xy' + ky = 0$ has indicial roots that are real exactly when $k \le 9$ (since the roots sum to $-6$ and multiply to $k$). For how many integers $k$ with $1 \le k \le 9$ are BOTH indicial roots negative, meaning both Frobenius solutions $x^{r}$ blow up as $x \to 0^+$?