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The real number k for which the equation...

The real number k for which the equation, `2x^3+""3x""+""k""=""0` has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

A

lies between 1 and 2

B

lies between 2 and 3

C

lies between -1 and 0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=2x^(3)++3x+k`
On differentiating w.r.t.x, we get
`f'(x)f=6x^(2)+3gt0,AAx in R`
`impliesf(x)` is strictly increasing function.
`implies f(x)=0` has only one real root so two roots are not possible.
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