Question

Let α, β be the roots of the equation $(x - a)(x - b) = c$, $c \neq 0$, then the roots of the equation $(x - \alpha)(x - \beta) + c = 0$ are

• A. a, c
• B. b, c
• C. a, b
• D. a, d

Answer 1

Answer: (C)

a, b

Answer 2

Since α, β are the roots of $(x - a)(x - b) = c$ i.e. of

$x^{2} - (a + b)x + ab - c = 0$

∴ $\alpha + \beta = a + b$ ⇒ $a + b = \alpha + \beta$ and $\alpha\beta = ab - c$

⇒ $ab = \alpha\beta + c$

∴ a, b are the roots of $x^{2} - (\alpha + \beta)x + \alpha\beta + c = 0$

⇒ $(x - \alpha)(x - \beta) + c = 0$

Hence (3) is the correct answer