In order that the equation 2ax(ax+nc) +(n^2-2)c^2=0 may have real roots , n belongs to interval

Answers (1)

Solution:   The given equation  is 2ax(ax+nc)+(n^2-2)c^2=0

   It has real roots , so 

               \ \ Rightarrow hspace1cm Dgeq 0Rightarrow (2anc)^2-4cdot 2a^2(n^2-2)c^2geq 0\ \ Rightarrow hspace1cmn^2-2(n^2-2)geq0\ \ Rightarrow hspace1cmn^2-4leq0Rightarrow (n+2)(n-2)leq0\ \ Rightarrow hspace1cmnin [-2,2] \ \ ecause hspace1cm4a^2c^2 hspace0.2cmis hspace0.2cmpositive

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