Question

If two quadratic equations
$x^2+bx-1=0\&x^2+x+b=0$ have a root in common, then $b^3+3b=$

• A. $1$​​​​​
• B. $0$
• C. $-1$

Answer 1

The correct option is B $0$

Let $\alpha$ be the common root of given equations, then
${\alpha }^2+b\alpha -1=0\cdots \left(1\right)$
and ${\alpha }^2+\alpha +b=0\cdots \left(2\right)$
Subtracting (2) from (1), we get
$(b-1)\alpha -(b+1)=0$
$\Rightarrow \alpha =\frac{b+1}{b-1}$
Substituting this value of $\alpha$ in equation (1) , we get
$(\frac{b+1}{b-1}{)}^2+b(\frac{b+1}{b-1})-1=0$
$\Rightarrow b^3+3b=0$