Question

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

Answer 1

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