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 $2$

Answer 1

The correct option is C does not exist

If

$2x^3+3x+k=0$ has 2 distinct real roots in $[0,1]$, then $f^{\prime }\left(x\right)$ will change sign once in the interval.

But,

$f^{\prime }\left(x\right)=6x^2+3>0$ for $0\le x\le 1$

So, no value of $k$ exists for which there are two real roots of the equation in $[0,1]$