need to find two integers for -26 product and sum of -11

Question

The product is -26 and the sum is -11 what are the two integers?

Answer 1

If you need to write an equation for it, then write out just what they say:

 

First let the two integers be x and y:

 

xy = -26

x + y = -11

 

Now solve this using substitution:

 

y = -x - 11

x(-x - 11) = -26

-x(x + 11) = -26

x(x + 11) = 26

x² + 11x = 26

x² + 11x - 26 = 0

 

Now, you could solve this by factoring, but to do that, you're almost in the same boat as you were at the beginning.  But anyway, factoring leads to:

 

(x + 13)(x - 2) = 0

x = -13 or x = 2.

 

Now go back to the original equations.

 

xy = -26

if x = -13, then y = 2

if x = 2, then y = -13

 

So no matter which solution you choose for x, the two integers come out to -13 and 2.

 

But you could also solve the original problem by "observation."

 

There aren't many pairs of integers whose product is -26 -- just the following:

 

-1, 26

1, -26

-2, 13

2, -13

 

Now look at these and see in which pair the two numbers add up to -11.  The only one is 2 and -13, and that's the same answer we got using the equation.

 

Answer 2

Jennifer,

 

 Let x be the first integer and y be the second integer. You need their product to be -26 and their sum to be -11, meaning

 

 xy=-26

 

 x+y=-11.

 

You have two equations and two unknowns. You can use any method you like from here to solve this system of equations (I would suggest the substitution method). Best of luck!