ODE — stability of constant-coefficient equations

For any solution $\phi$ of $y"+a_1y'+a_2y=0$ ($a_1,a_2$ constants): (I) $\phi\to0$ as $x\to\infty$ if the real parts of the roots of the characteristic polynomial are negative. (II) $\phi\to0$ as $x\to\infty$ if the real parts of the roots are positive. Then: