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)

does not exist

Answer 2

Let $f (x) = 2x^3 + 3x + k, f'(x) = 6x^2 + 3 > 0$ 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.