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

Options

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

Answer

D

Explanation

We have,
`therefore" "f(x) = 2x^(3) + 3x + k`
`rArr" "f'(x) = 6x^(2) + 3 gt 0` for all x `in` R
`rArr" "f(x)` is strictly increasing on R
`rArr" "f(x) = 0` may have only one real root
So, there is no value of k for which f(x) has two distinct real roots in [0, 1].