Question

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

Answer 1

Let $f\left(x\right)=2x^3+3x+k{f}^{\prime }\left(x\right)=6x^2+3>0,forallx\in R$

So f'(x) is strictly increasing function and hence f(x)=0, has only one real root, so two roots are not possible.