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