SOLUTION: What is the value of k so that the equation 2x2 + 4x - 17 = kx has roots numerically equal but opposite in sign?

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Question 998656: What is the value of k so that the equation 2x2 + 4x - 17 = kx has roots numerically equal but opposite in sign?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B4x-17=kx

2x%5E2%2B4x-17-kx=0
2x%5E2%2B4x-kx-17=0
2x%5E2%2B%284-k%29x-17=0

x=%28%28k-4%29%2B-+sqrt%28%284-k%29%5E2-4%2A2%2A%28-17%29%29%29%2F%282%2A2%29

x=%28k-4%2B-+sqrt%2814-8k%2Bk%5E2%2B136%29%29%2F4

x=%28k-4%2B-+sqrt%28k%5E2-8k%2B150%29%29%2F4-----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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%28k-4-sqrt%28k%5E2-8k%2B150%29%29%2F4%2B%28k-4%2Bsqrt%28k%5E2-8k%2B150%29%29%2F4=0

%28k-4-sqrt%28discrim%29%2Bk-4%2Bsqrt%28discrim%29%29%2F4=0

%282k-8%29%2F4=0

2k-8=0

k-4=0

highlight%28k=4%29