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`

Options

A. `sqrt(2)`
B. `-isqrt(3)`
C. `isqrt(5)`
D. `sqrt(2)`

Answer

B

Explanation

Let `alpha` be a common root of the given equations. Then,
`alpha^(2)+b alpha - 1 = 0" "(i)`
`alpha^(2)+alpha+b = 0" "...(ii)`
On subtracting, we get `(b-1) alpha = b+1 rArr alpha = (b+1)/(b-1)`
Substituting the value of `alpha` in (i), we get `(b+1)^(2)+b(b+1)(b-1)-(b-1)^(2)=0`
`rArr" "b(b^(2)-1)+4b = 0`
`rArr" "b(b^(2)+3)=0 rArr b = 0, +- isqrt(3)`