The sum of two integers is 5. Their product is -6. What are the integers? F. -1, 6       G. 2,3 H. 1,-6        J. 2,-3  

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Let the integers be x and y.

If the sum of the integers is 5 then x+y=5.

If the product of the integers is -6 then xy=-6.

From the first equation we have y=5-x. Substituting into the second equation yields:

x(5-x)=-6

`5x-x^2=-6`

`x^2-5x-6=0`

`(x-6)(x+1)=0` You could also solve with the quadratic formula

so x=6 or x=-1.

If x=6 then y=-1 and if x=-1 then y=6

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The two integers are 6 and -1; the answer is F

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In a multiple choice situation you can try the answers to see which works. In H the sum is -5, in G the product is 6, while in J the sum is -1

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