Question

If one of the roots of the equation $x^{2} + ax + b = 0$ and

$x^{2} + bx + a = 0$ is coincident. Then the numerical value of

$(a + b)$ is

• A. 0
• B. – 1
• C. 1
• D. 5

Answer 1

Answer: (B)

– 1

Answer 2

If α is the coincident root, then $\alpha^{2} + a\alpha + b = 0$ and

$\alpha^{2} + b\alpha + a = 0$

⇒ $\frac{\alpha^{2}}{a^{2} - b^{2}} = \frac{\alpha}{b - a} = \frac{1}{b - a}$

$\alpha^{2} = - (a + b)$, $\alpha = 1$ ⇒ $- (a + b) = 1$ ⇒ $(a + b) = - 1$