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# If is an integer and the root(s)

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If is an integer and the root(s) of the quadratic expression 1/2*x^2 + sx - 1/3 = 0 are integers, find the sum of all possible values of s.

Oct 25, 2020

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If is an integer and the root(s) of the quadratic expression 1/2*x^2 + sx - 1/3 = 0 are integers, find the sum of all possible values of s.

Hello Guest!

$$\frac{1}{2}x^2+sx-\frac{1}{3}=0$$

a           b        c

$$x = {-s \pm \sqrt{s^2-4\cdot 0.5\cdot \frac{1}{3}} \over 2\cdot 0.5}\\ x =-s\pm \sqrt{s^2-\frac{2}{3}}$$

$$s\in \{-3\mathbb Z\}\ |\ (x =-s+ \sqrt{s^2-\frac{2}{3}})$$

$$s\in \{+3\mathbb Z\}\ |\ (x =-s- \sqrt{s^2-\frac{2}{3}})$$

Incorrect. Question cannot be solved.

!

Oct 25, 2020
edited by asinus  Oct 25, 2020
edited by asinus  Oct 25, 2020