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),i=sqrt(-1)`
C. `isqrt(5),i=sqrt(-1)`
D. `sqrt(2)`

Answer

B

Explanation

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)`.