Question

Two negative integers have a sum of -12 and a product of 11. What are the integers?

Answer 1

ab = 11
a + b = -12

use substitutionn: b = -12 - a

a(-12 - a) = 11

so -a(12 + a) = 11

so 12a + a^2 = -11

so a^2 + 12a + 11 = 0

so (a + 11)(a + 1) = 0

so a = -11, -1

therefore b = -1, -11

thus the two numbers are -1 and -11

Answer 2

Thanks.