The value of $$a$$ for which the equations $$x^3+a x+1=0$$ and $$x^4+a x^2+1=0$$ have a common root is

If $$a$$ is a positive integer such that roots of the equation $$7 x^2-13 x+a=0$$ are rational numbers, then the smallest possible value of $$a$$ is

The sum of the roots of the equation $$e^{4 t}-10 e^{3 t}+29 e^{2 t}-22 e^t+4=0$$ is