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If $s$ is an integer and the root(s) of the quadratic expression $\frac{1}{2}x^2+sx-\frac{1}{2}$ are integers, find the sum of all possible values of $s$.

 Jan 22, 2018
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\($\frac{1}{2}x^2+sx-\frac{1}{2}$\)

 

The sum of the roots  is   -s / (1/2)  =   -2s

And the product of the roots is   (-1/2) / (1/2)   =  -1      (2)

 

If the roots are integers then, by (2), one must be  -1  and the other is  1 

 

So...   s  must be 0

 

 

cool cool cool

 Jan 22, 2018

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