Question

If the equations $x^2 + bx - 1 = 0 $ and $x^2 + x + b = 0$ have a common root different from $-1$, then $|b|$ is equal to :

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

Answer 1

Answer: (D)

$x^{2}+bx-1=0$ common root
$x^{2}+x+b=0$
$\frac{---}{x=\frac{b+1}{b-1}}$
Put $x=\frac{b+1}{b-1}$______in equation $\left(2\right)$
$\left(\frac{b+1}{b-1}\right)^{2}+\left(\frac{b+1}{b-1}\right)+b=0$
$\left(b+1\right)^{2}\left(b+1\right)\left(b-1\right)+b\left(b-1\right)^{2}=0$
$b^{2}+1+2b+b^{2}-1+b\left(b^{2}-2b+1\right)=0$
$2b^{2}+2b+b^{3}-2b^{2}+b=0
b^{3}+3b=0$
$b\left(b^{2}+3\right)=0$
$b^{2}=-3$
$b=\pm\sqrt{3}i$
$\left|b\right|=\sqrt{3}$