The given problem has 4 different solutions as below.
Given that the product of the two numbers is -100.
And one of the factors is less than 10 and more than 0.
Assume c and d are the two required numbers.
Then we have cd = -100, here 0 < c <10.
We know that the factors of 100, which are less than 10 and greater than 0 are 1, 2, 4, and 5.
When c = 1, we get 1 x d = -100 ⇒ d = -100
When c = 2, we get 2 x d = -100 ⇒ d = -100/2 = -50
When c = 4, we get 4 x d = -100 ⇒ d = -100/4 = -25
When c = 5, we get 5 x d = -100 ⇒ d = -100/5 = -20
So, the other factors corresponding to the above factors are -100, -50, -25, and -20.
Therefore, the given problem has 4 different solutions as below.
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