If one root of the equation 2x^2 + 10x + k = 0 is -2, what is the other root?
Plug in -2 for x and solve for k:
$\displaystyle \begin{aligned}
2x^2 + 10x + k &= 0 \\
2(-2)^2 + 10(-2) + k &= 0 \\
8 - 20 + k &= 0 \\
-12 + k &= 0 \\
k &= 12
\end{aligned}$
For a quadratic equation $\displaystyle ax^2 + bx + c = 0$ the sum of the two roots (I'll call them r1 and r2) is -b/a:
$\displaystyle \begin{aligned}
r_1 + r_2 &= -\frac{10}{2} \\
-2 + r_2 &= -5 \\
r_2 &= -3
\end{aligned}$
So the other root is -3.