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Show that the equation a z^3+b z^2+ barb...

Show that the equation `a z^3+b z^2+ barb z+ bara =0` has a root `alpha` such that `|alpha|=1,a ,b ,z and alpha` belong to the set of complex numbers.

A

`1//4`

B

`1//2`

C

`5//4`

D

`3//4`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `aalpha^(2)+balpha+1=0` ……….`(i)`
`implies barabaralpha^(2)+barbbaralpha+1=0`
`implies alpha^(2)+barbalpha+bara=0` (as `|alpha|=alphabaralpha=1`) ……….`(ii)`
From `(i)` and `(ii)`
`(alpha^(2))/(barab-barb)=(alpha)/(1-|a|^(2))=(1)/(abarb-b)implies|abarb-b|=1-|a|^(2)=1-(1)/(4)=(3)/(4)`
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