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Let S be the set of all real numbers a such that the function (x^2+5x+a)/(x^2+7x-44) can be expressed as the quotient of two linear functions. What is the sum of the elements of S?

 Jun 27, 2018
 #1
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Note that  x^2  + 7x  - 44   can be factored as   ( x + 11) ( x - 4)

 

So   x^2 + 5x + a     could be  ( x + 11) ( x - 6)   and a  = -66

Or ..... x^2 + 5x + a  could be  ( x - 4) (x + 9)  and a  = -36

 

Note that in the first case   the  quotient is  ( x - 4)  /( x - 6)

And in the second case the quotient is  ( x + 11) / ( x + 9)

 

So...S  = ( -66, -36)   and the sum of its elements is  -102

 

 

cool cool cool

 Jun 27, 2018

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