Question

If the difference between the corresponding roots of

$x^{2} + ax + b = 0$ and $x^{2} + bx + a = 0$ is same and $a \neq b$, then

• A. $a + b + 4 = 0$
• B. $a + b - 4 = 0$
• C. $a - b - 4 = 0$
• D. $a - b + 4 = 0$

Answer 1

Answer: (A)

$a + b + 4 = 0$

Answer 2

$\alpha + \beta = - a$, $\alpha\beta = b$ ⇒ $\alpha - \beta = \sqrt{a^{2} - 4b}$ and $\gamma + \delta = - b$, $\gamma\delta = a$ ⇒ $\gamma - \delta = \sqrt{b^{2} - 4a}$

According to question, $\alpha - \beta = \gamma - \delta$ ⇒ $\sqrt{a^{2} - 4b} = \sqrt{b^{2} - 4a}$ ⇒ $a + b + 4 = 0$