Suppose $a_1$, $b_1$, $c_1$, $a_2$, $b_2$, and $c_2$ are all positive real numbers. If both $a_1x^2 +b_1x+c_1=0$ and $a_2x^2+b_2x+c_2=$ are solvable in real numbers. Show that their roots must be all negative. Furthermore, prove equation $a_1a_2x^2+b_1b_2x+c_1c_2=0$ has two negative real roots too.