Question

If $x^2+ax+b=0,x^2+bx+a=0(a\ne 0)$ have a common root then $a+b$

• A. $3$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

The correct option is D $-1$

Let $x$ be the common root then it must satisfy both quadratic equations.

$x^2+ax+b=0.....\left(1\right),x^2+bx+a=0....\left(2\right)$

Subtract (1) by (2)

$x(a-b)+(b-0)=0\Rightarrow x=1$

Substitute value of $x$ in $\left(1\right)$

$1+a+b=0\Rightarrow a+b=-1$.