Question

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

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

Answer 1

The correct option is B

a+b = -1

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

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

then $\alpha$ will satisfy for both the equations

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

$\alpha =1$

$\alpha =1$ is the common root from equation 1

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

1 + a + b = 0

a + b = -1