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Question

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


A
lies between 2 and 3
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B
lies between 1 and 0
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C
does not exist
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D
lies between 1 and 2
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Solution

The correct option is C does not exist
If 
$$2x^{3}+3x+k=0$$ has 2 distinct real roots in $$[0,1]$$, then $$f'(x)$$ will change sign once in the interval.  
But, 
$$f'(x)=6x^{2}+3>0$$ for  $$0\leq x\leq1$$
So, no value of $$k$$ exists for which there are two real roots of the equation in $$[0,1]$$

Mathematics

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