Question

S squared + 10s + 21 = 0

Answer 1

$s_{1}=-3, s_{2}=-7$

1) Let's solve this quadratic equation by the quadratic formula.

$\begin{gathered} s^2+10s+21=0 \\ \\ s=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ s_=\frac{-10\pm\sqrt{10^2-4\cdot\:1\cdot\:21}}{2} \\ \\ s=_\frac{-10\pm\:4}{2} \\ \\ s_1=\frac{-10-4}{2}=-\frac{14}{2}=-7 \\ \\ s_2=\frac{-10+4}{2}=\frac{-6}{2}=-3 \end{gathered}$

Note that this quadratic equation generated two different roots since the Discriminant is greater than 0.

2)Thus the answer is:

$s_1=-3,\:s_2=-7$