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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) `isqrt5` (d) `sqrt2`

A

` - sqrt(2)`

B

`-i sqrt(3)`

C

`sqrt(2)`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
` x^(2) + bx - 1 = 0 `
`x^(2) + x + b = 0 `
Subtracting, we get ` (b - 1) x - 1 - b = 0 ` (1)
`rArr x = (b + 1)/(b- 1) `
This value of x satisfies equation (1)
`rArr x = ((b + 1) ^(2))/((b- 1) ^(2)) + (b + 1)/(b- 1) + b = 0 `
`rArr b = sqrt(3i), - sqrt(3i), 0` .
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