Question 998656
{{{2x^2+4x-17=kx}}}


{{{2x^2+4x-17-kx=0}}}
{{{2x^2+4x-kx-17=0}}}
{{{2x^2+(4-k)x-17=0}}}


{{{x=((k-4)+- sqrt((4-k)^2-4*2*(-17)))/(2*2)}}}


{{{x=(k-4+- sqrt(14-8k+k^2+136))/4}}}


{{{x=(k-4+- sqrt(k^2-8k+150))/4}}}-----Is that discriminant a perfect square?
2*75,3*50,5*30,6*25,10*15, does not seem to be; this will actually not be important.


The requirement is that the roots, the possible x values, must be equal in size but opposite
in their signs.  That is, they are additive inverses of each other.
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{{{(k-4-sqrt(k^2-8k+150))/4+(k-4+sqrt(k^2-8k+150))/4=0}}}


{{{(k-4-sqrt(discrim)+k-4+sqrt(discrim))/4=0}}}


{{{(2k-8)/4=0}}}


{{{2k-8=0}}}


{{{k-4=0}}}


{{{highlight(k=4)}}}