Question

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

Answer 1

-11 and -1

Explanation:

x^2 - 12x + 11 = 0

factorize

(x - 11 ) × (x - 1)

then

x^2 - 12x + 11 = (x - 11 ) × (x - 1)

so your answer is

-11 and -1

------------------------------

-11 × -1 = 11

-11 + -1 = -12

Answer 2

11 and -1

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.