Question

Write a pair of integers whose product is -36 and whose sum is 16

Answer 1

Heya


The two integers are 18 and -2.


I have attached a pic of the solution.



Hope this helps

Answer 2

Answer:

Let x and y be the integers.

As per the statement:

Product of integers is -36

⇒$xy = -36$

or

⇒$x = -\frac{36}{y}$                    .....[1]

It is also given their sum is 16:

⇒x+y = 16                    .....[2]

Substitute equation [1] into [2] we have;

$-\frac{36}{y}+y = 16$

⇒$-36+y^2 = 16y$

⇒$y^2-16y-36=0$

Factorize the polynomial.

$y^2-18y+2y-36=0$

⇒$y(y-18)+2(y-18)=0$

⇒$(y+2)(y-18)=0$

By zero product property we have;

y+2 = 0 and y-18 = 0

⇒y =-2 and y= 18

Substitute in [1] we have;

for y = -2

then;

$x = -\frac{36}{-2}= 18$      

Similarly;

For y = 18

⇒x = -2

therefore. the pairs of integers whose product is -36 and whose sum is 16 are: (-2, 18) or (18, -2)