I could use some help on this problem I have to find the integer pairs for two different given products and sums:  The products are 45 and -34 and the sums are -14 and -15 Thanks

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Let us say the two numbers are A and B respectively.

Sum of A and B is 45.

`A+B = -14-----(1)`

Product of A and B is;

`AB = 45 ----(2)`

 

From (1) we can get `A = -B-14 = -(B+14)`

`AB = 45`

`-(B+14)B = 45`

`-B^2-14B-45 = 0`

`B^2+14B+45 = 0`

`B^2+9B+5B+45 = 0`

`B(B+9)+5(B+9) = 0`

`(B+9)(B+5) = 0`

Solving the above equation yields B = -9 and B = -5.

Substituting these values on (1) will give A = -5 and A = -9.

 

So the two numbers are -9 and -5.

 

Note

You can do the next in the same way.

The answers would be -17 and 2.

 

Sources:

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