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2015-09-21T23:37:34+05:30

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     f (x) =  14 x²  -  42  k² x - 9
   root =   [ 42 k²  + -  √ (42² k⁴ + 504) ] / 28
           = 3 * [ 7 k² + - √(7² k⁴ + 14) ] / 14

  since k² is non negative,
       7 k²  <  √ (7 k⁴ + 14)
  so we will have one root negative and one root positive.
  This is true for any real  value of  k.
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