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?

DanielCai Jun 27, 2018

#1**+1 **

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

CPhill Jun 27, 2018