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If one root is cube of the other of equa...

If one root is cube of the other of equation `81x^2 +kx+256=0` then value of k is equal to (A) `100` (B) `-300` (C) `-81` (D) `400`

A

100

B

144

C

`-81`

D

`-300`

Text Solution

Verified by Experts

The correct Answer is:
D
Given quadratic equation is
`81x^(2)+kx+258=0`
Let one root be `alpha,` then other is `alpha^(3).`
Now, `alpha+alpha^(3)=-k/81and alpha.alpha^(3)=(256)/(81)`
`" ""["therefore "for" ax^(2)+bx+c=0 "sum or roots"=-b/a "and product of roots"=c/a"]"`
`=alpha^(4)=((4)/(3))^(4)impliesalpha=+-4/3`
`thereforek =-81alpha(1+alpha^(3))`
`=-81 alpha (1+a^(2))`
`=81 (+-(4)/(3))(1+(16)/(9))=+-300`
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