Question

If $a\ne b,$ if the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ have a common root, the value of $(a+b)$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is A $-1$

${\alpha }_1+{\beta }_1=-a$ ${\alpha }_2+{\beta }_2=-b$

Let ${\alpha }_1={\alpha }_2=\alpha$

$\alpha +{\beta }_1=a$ ; $\alpha +{\beta }_2=-b$

$\alpha {\beta }_1=b$ $\alpha {\beta }_2=a$

$\frac{{\beta }_1}{{\beta }_2}=\frac{b}{a}$

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

$(b+a)=-\alpha =-1$