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Find the sum of all integral values of c with c$$\le$$25 for which the equation $$y=x^2-7x-c$$ has two rational roots.

Mar 11, 2020

#2
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Find the sum of all integral values of c with $$c\le 25$$ for which the equation y=x^2-7x-c  has two rational roots.

The discriminant must equal a perfect square (not 0).

$$\triangle=49+4c$$

$$\triangle=49-48=1\qquad c=-12\\ \triangle=49-40=9\qquad c=-10\\ \triangle=49-24=25\qquad c=-6\\ \triangle=49-0=49\qquad c=0\\ \triangle=49+32=81\qquad c=16\\ \triangle=49+72=121\qquad c=18\\$$