Question

A value of b for which the equations
$x^2+bx-1-0$
$x^2+x+b=0,$
have one root in common is -

• A. -2
• B. $i-\sqrt{3}$
• C. $i\sqrt{5}$
• D. $\sqrt{2}$

Answer 1

The correct option is A -2

$\Rightarrow {\alpha }^2+b\alpha -1=0$

& ${\alpha }^2+\alpha +b=0$

(-)

_________________

$b\alpha -\alpha -1-b=0$

$\Rightarrow \alpha =\frac{b+1}{b-1}$

$\Rightarrow {\left(\frac{b+1}{b-1}\right)}^2+b\left(\frac{b+1}{b-1}\right)=1$

$\Rightarrow (b+1{)}^2+b(b+1\left)\right(b-1)=b-1$

$\Rightarrow b^2+2b+1+b^3-b=b-1$

$\Rightarrow b^3+b^2+2=0\Rightarrow b=-2$