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

Solution

## The correct option is C does not existIf $$2x^{3}+3x+k=0$$ 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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