If I have an equation of degree 2 or 3 and one of the coefficients is unknown, how to find that coefficient giving that one of the poles is given.

Question

For example, $S^3 + 3S^2 + 18S + K$

Given that one of the roots is $-10$. How would you find K that satisfies this condition?

Answer 1

Hint:

substitute $S=-10$ in $S^3 + 3S^2 + 18S + K$ and find $k$.

Answer 2

If one of the roots is $-10$, then that means exactly that $$ (-10)^3 +3(-10)^2+18(-10)+K=0 $$ Now you can just calculate.

Answer 3

It worked! K = 880. I tried solving it with my calculator and it gave me the roots which one of them is -10.