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if x^3+ax+1=0 and x^4+ax^2+1=0 have comm...

if `x^3+ax+1=0 `and `x^4+ax^2+1=0` have common root then the exhaustive set of value of `a` is

A

`a=2`

B

`a=-2`

C

`a=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `x^(3)+ax+1=0`
or `x^(4)+ax^(2)+x=0`……………..i
and `x^(4)+ax^(2)+1=0`……………ii
From Eqs. (i) and (ii) we get
`x-1=0`
`impliesx=1`
Which is a common root.
`:.1+a+1=0`
`impliesa=-2`
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