Question

The quadratic equations $x^2+ax+b=0$ and $x^2+bx+a=0$, have one common root and $a\ne b$, then

• A. $a+b=-2$
• B. $a+b=2$
• C. $a+b=-1$
• D. $a+b=1$

Answer 1

The correct option is C

$a+b=-1$

$x^2+ax+b=0$.................(1)

$x^2+bx+a=0$ .................(2)

then $\alpha$ will satisfy for both the equations

${\alpha }^2+a\alpha +b={\alpha }^2+b\alpha +a\Rightarrow \alpha (a-b)=a-b$

$\Rightarrow \alpha =1$

$\alpha =1$ is the common root from equation $\left(1\right)$

$(1{)}^2+a(1)+b=0$

$\Rightarrow 1+a+b=0$

$\Rightarrow a+b=-1$