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MATH / Let S be the set of all real numbers α such that the function (x²+5x+α)/(x²+7x−44)can be expressed as a quotient of two linear functions. What is the sum of the elements of S?

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problem

Let SS be the set of all real numbers α\alpha such that the function x2+5x+αx2+7x−44\frac{x^2+5x+\alpha}{x^2 + 7x - 44}can be expressed as a quotient of two linear functions. What is the sum of the elements of SS?
Plain-text mathematical notation (without MathML)
Let S be the set of all real numbers α such that the function (x²+5x+α)/(x²+7x−44)can be expressed as a quotient of two linear functions. What is the sum of the elements of S?
Original LaTeX notation
Let $S$ be the set of all real numbers $\alpha$ such that the function \[\frac{x^2+5x+\alpha}{x^2 + 7x - 44}\]can be expressed as a quotient of two linear functions. What is the sum of the elements of $S$?

level

Level 5

type

Algebra

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Source and history

task_id
e15e46c6-ddf9-5a35-a655-b5c46e0e11cf
task_key
algebra--test--e15e46c6-ddf9-5a35-a655-b5c46e0e11cf
task_revision_id
1
config / split
algebra / test

Official source

initial import