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JEE Main 20137 April
Exam
JEE Main
Year
2013
Date
7 April
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2013 · 7 April · Mathematics · Quadratic Equation

The real number k for which the equation, 2 x ^ 3 + 3x + k = 0 has...

The real number kk for which the equation, 2x3+3x+k=02{x}^{3} + 3x + k = 0 has two distinct real roots in [0,1][ 0, 1 ] belongs to

Options

  1. Alies between −1- 1 and 00.
  2. Bdoes not exist.
  3. Clies between 11 and 22.
  4. Dlies between 22 and 33.

Correct answer

B. does not exist.

Step-by-step solution

Given f(x)=2x3+3x+xf\left(x\right) = 2{x}^{3} + 3x + x

⇒f′(x)=6x2+3⇒ {f}^{'}\left(x\right) = 6{x}^{2} + 3

As f′(x)>0{f}^{'}\left(x\right) > 0 for all xx.

⇒f(x)⇒ f\left(x\right) is a strictly increasing function for all xx.

Hence f(x)=0f\left(x\right) = 0 cannot have more than one root.

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