C. Find two numbers that multiply to 11 and add to - 12.

11 and - 1

Step-by-step explanation:

Represent the numbers by x and y. Then x*y = 11 and x + y = - 12.

Let's eliminate y temporarily. Solving the first equation for y yields 11/x. Substituting this 11/x for y in the second equation yields x + 11/x = - 12.

Let's clear out the fractions by multiplying all of these terms by x:

x^2 + 11 = - 12x, or x^2 + 12x + 11 = 0.

This factors to (x + 11) (x + 1) = 0, so the roots are - 11 and - 1.

Note that - 11 and - 1 multiply to + 11 and that - 11 and - 1 add to - 12.