Question

$a+b+1=0$ is the condition for the quadratic equations $x^2+ax+b=0$ and $x^2+bx+a=0$ to have a common root.

• A. True
• B. False

Answer 1

The correct option is A True

Let ${}^{\prime }{\alpha }^{\prime }$ be the common root then ${\alpha }^2+a\alpha +t=0$ .......$\left(1\right)$

${\alpha }^2+b\alpha +a=0$ .......$\left(2\right)$

$\left(2\right)$ - $\left(1\right)$

$\Rightarrow (b-a)\alpha +(a-b)=0$

$\Rightarrow \alpha =1$

but $\alpha =1$ in $\left(1\right)$ in $\left(2\right)$ we get

$a+b+1=0$.