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Question

The values of p for which the equation x26|x|+5|p|=0 has exactly four real roots, is
  1. (0,2)
  2. (5,5)
  3. (2,10)
  4. (5,10)


Solution

The correct option is B (5,5)
For four real roots, t26t+5|p|=0 (|x|=t) must have two distinct positive roots.
Let f(t)=t26t+5|p|
Δ>0 and f(0)>0
pR and 5|p|>0
p(5,5) 

 

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