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Suppose $\mathrm{k}$ is any integer such that the equation $2 x^{2}+k x+5=0$ has no real roots and the equation $x^{2}+(k-5) x+1=0$ has two distinct real roots for $\mathrm{x}$. Then, the number of possible values of $\mathrm{k}$ is

1. $7$
2. $9$
3. $8$
4. $13$

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