Question

Let $\alpha, \beta$ be the roots of the equation,$(x - a) (x - b) = c, c \ne 0$.Then the roots of the equation $(x - \alpha) \, (x - \beta) + c = 0$ are

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

Answer 1

Answer: (C)

a, b

Answer 2

Given, $\alpha, \beta$ are the roots of (x - a) (x - b) - c = 0
$\Rightarrow (x - a) (x - b) - c = (x - \alpha) \, (x - \beta)$
$\Rightarrow (x - a) \, (x - b) = (x - \alpha) \, (x - \beta) + c$
$\Rightarrow$ a, b are the roots of equation $(x - \alpha) \, (x - \beta) + c$