Question

If one of the roots of the equation $x^2+ax+b=0$ and $x^2+bx+a=0$ is coincident, then the numerical value of $(a+b)$ is

• A. \N
• B. -1
• C. 2
• D. 5

Answer 1

The correct option is B -1

If $\alpha$ is the coincident root, then
${\alpha }^2+a\alpha +b=0$ and ${\alpha }^2+b\alpha +a=0$
$\Rightarrow \frac{a^2}{a^2-b^2}=\frac{a}{b-a}=\frac{1}{b-a}$
$\Rightarrow {\alpha }^2=-(a+b);\alpha =1\Rightarrow -(a+b)=1\Rightarrow (a+b)=-1$