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The number of integers n for which 3x^(3...

The number of integers n for which `3x^(3)-25x +n=0` has three real roots is-

A

1

B

25

C

55

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
`x(3x^(2)-25)=-n`
`3x(x^(2)-(25)/(3))=-n`
`3 x (-xsqrt((25)/(3)))(x+sqrt((25)/(3)))=-n`

`:. n in(-(250)/(9),(250)/(9))`
`:.` But `n in I`
Total integr =55
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