Find two integers whose product is -18 and whose sum is 3.

Question

pre algebra involving intergers

Answer 1

Question: Find two integers whose product is -18 and whose sum is 3.

Let the two integers be x and y. Then

x + y = 3   -- their sum is 3

xy = -18   -- their product is -18

From the 1st eqn, x = 3 - y. So substitute this into the 2nd equation. This gives

(3 - y)y = -18   -- multiply out

3y - y^2 = -18   -- arrange into a standard quadratic

y^2 - 3y - 18 = 0   -- now factorise

(y + 3)(y - 6) = 0

So, y = -3, or y = 6

And x = 3 - y

So, x = 6, or x = -3

In other words. the two integers are: -3 and 6