How to factor $ s^2LC + sRC + 2$

Question

or $$ s^2+s\frac{R}{L}+\frac{2}{LC}=0 $$

Is there any way? I can't find out. Thanks in advance.

Answer 1

$$s^2+s\frac{R}{L}+\frac{2}{LC}=\left(s-\frac{-\frac RL+\sqrt{\frac{R^2}{L^2}-\frac{8}{LC}}}{2}\right)\left(s-\frac{-\frac RL-\sqrt{\frac{R^2}{L^2}-\frac{8}{LC}}}{2}\right)$$

Answer 2

HINT:

We can complete the square by writing

$$s^2+\frac RL s+\frac2{LC}=\left(s+\frac{R}{2L}\right)^2-\left(\frac{R^2}{4L^2}-\frac{2}{LC}\right)$$

Can you factor this?