The real number k for which the equation, 2 x 3 + 3 x + k = 0 has two distinct real roots in [ 0 ,   1…

The real number k for which the equation, 2x3+3x+k=0 has two distinct real roots in [0, 1] belongs to
  1. lies between -1 and 0.
  2. does not exist.
  3. lies between 1 and 2.
  4. lies between 2 and 3.

Solution

Given fx=2x3+3x+x

⇒f'x=6x2+3

As f'x>0  for all x.

⇒fx is a strictly increasing function for all x.

Hence fx=0 cannot have more than one root.

Asked in: JEE Main 2013 (07 Apr)

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