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Consider biquadratic equation 81x^(4) + ...

Consider biquadratic equation `81x^(4) + 216x^(3) + 216x^(2) +96x = 65`, whose roots are `a,b,c,d`. Given `a,b`, real roots and c,d are imaginary roots.
On the basis of above information, answer the followin questions:
The value of `(a+b)^(3) - (c+d)^(3)` is equal to-

A

`(-128)/(3)`

B

0

C

`(-64)/(3)`

D

`(-142)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
B
The given equation is ltbgt `(3x+2)^(4) = 81`
`implies ((3x+2)^(2)-9)((3x+2)^(2)+9)=0`
Let `a=(1)/(3),b=(-5)/(3),C=(-2)/(3)+i,d=(-2)/(3)-i`
Now,verfiy it
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