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The value of b for which the equation x^...

The value of `b` for which the equation `x^2+bx-1=0 and x^2+x+b=0` have one root in common is:

A

`-sqrt(2)`

B

`-isqrt(3),i=sqrt(-1)`

C

`isqrt(5),i=sqrt(-1)`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `alpha` be the common root.
Then `alpha^(2)+b aopha-1=0` and `alpha^(2)+alpha+beta=0`
implies|(1,b),(1,1)|xx|(b,-1),(1,b)|=|(-1,1),(b,1)|^(2)`
`implies(1-b)(b^(2)+1)=(-1-b)^(2)`
`impliesb^(3)+3b=0`
`:.b=0, isqrt(3),-isqrt(3)` where `i=sqrt(-1)`.
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