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Question

The real number k for which the equation2x3+3x+k=0 has two distinct real roots in [0,1]

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Solution

Let f(x)=2x3+3x+kf(x)=6x2+3>0,forallxR
So f'(x) is strictly increasing function and hence f(x)=0, has only one real root, so two roots are not possible.

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