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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

`-sqrt2`

B

`-isqrt3`

C

`I sqrt5`

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
If `a_(1)x^(2)+b_(1)x+c_(2)=0`
have a common real roots, then
`implies(a_(1)c_(2)-a_(2)c_(1))^(2)=(b_(1)c_(2)-b_(2)c_(1))(a_(1)b_(2)-a_(2)b_(1))`
`therefore{:(x^(2)+bx-1=0),(x^(2)+x+b=0):}` have a common root.
`implies(a+b)^(2)=(b^(2)+1)(1-b)`
`implies b^(2)+2b+1=b^(2)-b^(3)+1-b`
`impliesb^(3)+3b=0`
`thereforeb(b^(2)+3)=0`
`impliesb=0, pmsqrt3i`
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