Question

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

Answer 1

zero works by inspection

Answer 2

wat do u mean @satellite73

Answer 3

if you put \(b=0\) you get
\[x^2-1\] whose zeros are 1 and -1 and also \(x^2+x\) whose zeros are 0 and -1

Answer 4

they share one root, namely \(-1\)

Answer 5

the options are sqrt 2 isqrt3 i sqrt5

Answer 6

ooooh ok
go with \(i\sqrt{3}\)

Answer 7

hw...???

Answer 8

solve four equations
\[-b\pm\sqrt{b^2+4}=-1\pm\sqrt{1-4b}\]
one will give you \(b-0\) which is the answer i like
two are impossible
one has solution \(\pm i\sqrt{3}\)

Answer 9

let common root be y,
then
y ^2 +by - 1=0 = y^2 + y +b
=>by -1 = y +b
=>b = (y+1)/(y-1)

now (y -1)(y+1) = -by (from (1))
and y + 1 = -b/y (from (2))

=>y-1= y^2
y^2 - y +1 = 0

solve for y
and then for b..