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

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lies between 1 and 2

Lies between 2 and 3

lies between -1 and 0

Does not exist

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detailed solution

Correct option is D

clearly f′(x)=6x2+3>0,f(x) is increasing function f(x)=0 will have no real roots in [0,1]

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The real number k for which the equation, 2x3+3x+k=0 has two distinct real roots in [0,1]

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