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If the characteristic equation of the differential equation $$\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$$ has two equal roots, then the value of $\alpha$ are

1. $\pm 1$
2. $0,0$
3. $\pm j$
4. $\pm 1/2$