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# hard algebra 3

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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 $$S$$?

Sep 12, 2020

### 1+0 Answers

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$$x^2+7x-44=(x+11)(x-4)$$. So $$(x-4)(x+9)=x^2+5x-36\rightarrow a=-36$$. And $$(x+11)(x-6)=x^2+5x-66\rightarrow a=-66$$. So $$\boxed{a=-36,-66}$$

Sep 13, 2020