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If m is chosen in the quadratic equation (m2+1)x23x+(m2+1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is - 
  1. 85
  2. 45
  3. 43
  4. 83


Solution

The correct option is A 85
Sum of roots = 3m2+1  ( Sum of roots )max = 3
When m = 0
x23x+1 = 0
Let the roots of the equation is α and β
Then 
α+β = 3
αβ = 1
|α3β3| = |αβ||(α2+β2+αβ)|
= |((α+β)24αβ)||(α+β)2αβ|
= (94)(91)
= 85

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