Find two integers with the given product and sum. Show your complete working. a. product = 45, sum = 14b. product = 6, sum = −5

Sure, let's solve these problems one by one.

a. We are looking for two numbers x and y such that their product is 45 and their sum is 14. This can be written as a system of equations:

x*y = 45 x + y = 14

We can solve this system by substitution or elimination, but in this case, it's easier to just guess and check. The factors of 45 are 1, 3, 5, 9, 15, and 45. The pair that adds up to 14 is 5 and 9. So, the two numbers are 5 and 9.

b. We are looking for two numbers x and y such that their product is 6 and their sum is -5. This can be written as a system of equations:

x*y = 6 x + y = -5

Again, we can solve this system by substitution or elimination, but it's easier to just guess and check. The factors of 6 are 1, 2, 3, and 6. However, none of these pairs add up to -5. We need to consider negative factors as well. The pair that adds up to -5 is -2 and -3. So, the two numbers are -2 and -3.