Question

The equations $x^2 - ax + b = 0$ and $x^2 + bx - a = 0$ have a common root, then

• A. $a = b$
• B. $a + b = 1$
• C. $a + b = 0$ or $a-b=1$
• D. $a - b = 2.$

Answer 1

Answer: (C)

$a + b = 0$ or $a-b=1$

Answer 2

Let $\alpha$ be a common root of the given equations. $\therefore \, a^2 - a\alpha + b = 0$ and $a^2 + b\alpha - a= 0$. $\Rightarrow \, (a + b) \alpha - (a + b) = 0$ $\Rightarrow \, (a + b) (\alpha - 1) = 0$ $\Rightarrow \, a + b = 0$ or $\alpha = 1$