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=(-b\pm√(b^2-4ac))/(2a) \\ \\ s_=(-10\pm√(10^2-4\cdot\:1\cdot\:21))/(2) \\ \\ s=_(-10\pm\:4)/(2) \\ \\ s_1=(-10-4)/(2)=-(14)/(2)=-7 \\ \\ s_2=(-10+4)/(2)=(-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`