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The equation k+x^(3)e^(x+3)=0 has 2 dist...

The equation `k+x^(3)e^(x+3)=0` has 2 distinct real roots & `k` is a prime natural number, then the possible value of `k` is/are

A

11

B

13

C

31

D

37

Text Solution

Verified by Experts

The correct Answer is:
A, B
`y=x^(3)e^(x+3)=-k`
`y=x^(3)e^(x+3)`
`(dy)/(dx)=e^(x+3)(3x^(2)+x^(3))=0`
`impliesx=0, x=-3`
at `x=-3, y=-27`
For 2 distinct real roots, `kepsilon(0,27)`
So, prime value of `k` will be
`2,3,5,7,11,13,17,19,23=9`
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