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Let S be the set of all real numbers a such that the function (x^2+5x+a)/(x^2-10x-24) can be expressed as the quotient of two linear functions. What is the sum of the elements of S?

 Dec 3, 2020
 #1
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Note  that   x^2  -10x - 24  =  (x - 12) (x + 2)

 

So  we need to  have  that  a   =  6  or  x  = -204

 

If a = 6    we have that  x^2  + 5x  + 6  =  (x + 2) (x + 3)   and our quotient is  (x + 3) / ( x -12)

If a  = -204  we have that  x^2 + 5x - 204  = ( x -12) (x + 17)  and our quotient is  ( x +17) / (x + 2)

 

So

 

S  = { 6 , -204 }

 

And their sum  =  -198

 

cool cool cool

 Dec 3, 2020
edited by CPhill  Dec 3, 2020
edited by CPhill  Dec 3, 2020
 #2
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How did you derive a = 6 or -204 ?

Guest Dec 5, 2020

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