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Question

If 2λ1 and 2λ2 (λ1, λ2R and λ1λ2<0)
are the roots of the equation (a2+a+1)x24x+a=0, aR, then the set of values of a is
  1. (0,1)
  2. (3,1)
  3. (1,3)
  4. (3,0)


Solution

The correct option is A (0,1)
Let λ1>0 & λ2<0
One of the root is greater than 1 and one of the root is less than 1 but greater than 0
f(x)=(a2+a+1)x24x+a
It is an upward opening parabola.
f(0)>0 & f(1)<0

For f(0)>0a>0     (1)
For f(1)<0a2+2a+1<4
a2+2a3<0a(3,1)     (2)a(0,1)

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