Question

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

• A. lies between $1$ and $2$
• B. lies between $2$ and $3$
• C. lies between $-1$ and $0$
• D. does not exist

Answer 1

The correct option is D does not exist

Let $f\left(x\right)=2x^3+3x+k$
$f^{\prime }\left(x\right)=6x^2+3>0\forall k\in R$
Thus, $f\left(x\right)$ is strictly increasing function
Hence, $f\left(x\right)=2x^3+3x+k=0$ has only one real root, so two roots are not possible.