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

Answer: (C)

Let $f(x)=2x^3+3x+k,f^{\prime }(x)=6x^2+3>0$
Thus $f$ is strictly increasing. Hence it has atmost one real root. But a polynomial equation of odd degree has atleast one root.
Thus the equation has exactly one root.
Then the two distinct' roots; in any interval whatsoever is an impossibility. No such does not exists.