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Dimas [21]
4 years ago
11

The sum of two integers is -15. The product of the two integers is 54. What are those two integers a. -6 and -9 b. -6 and 9 c. 6

and 9
Mathematics
1 answer:
Bas_tet [7]4 years ago
3 0
Let the two integers be x and y respectively

Hence;
x + y =  - 15 \\  \\ xy = 54
From the first equation ;
x =  - 15- y
Substitute into the third equation
( - 15 - y)y = 54
Open up the bracket
- 15y -  {y}^{2}  = 54
Take everything to the right hand side of the equation and you'll have a quadratic equation
0 = 54 + 15y +  {y}^{2}
Solve the quadratic equation and you'll have two roots
y=  - 6 \: or \: y= -9
Substitute for each value of y in the first equation
Therefore:
x  + ( - 6) =  - 15 \:  \\ or \\  \: x + ( - 9) =  - 15
x - 6 =  - 15 \\ or \\ x - 9 =  - 15
x =  - 15 + 6 \\ or \\ x =  - 15 + 9

x =  - 9 \: or \: x =  - 6
Therefore the answer is A
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