What are two numbers that multiply to 24 and add to -19?

Answer 1

5

Answer 2

NONE.

This is a method used in factoring by grouping.

Let's solve this methodically: First, list all of the factors of 24, making sure not to forget negatives (two negatives multiply to a positive):

1 x 24, -1 x -24,

2 x 12, -2 x -12,

3 x 8, -3 x -8

4 x 6, -4 x -6

Now look at the list, adding all of the pairs together as you look at them.

As you can see, no pairs add to 19. Thus, if you are factoring a number, you must use wither the quadratic formula or completing the square. When factoring by grouping, fractions are NOT used.

___________________________

XY = 24. .......... 1

X+ Y = -19 ....... 2

From 2; Y = -19 - X

Substitute in 1; then:

X (-19 - X) = 24

X2 + 19X + 24 = 0

Solve for X then substitute in eq 2 to get Y value.