Question

(x–a) (x–b) + c = 0 (c ≠ 0), then the roots of the equation

(x – c – α) (x – c – β) = c are –

• A. a and b + c
• B. a + c and b
• C. a + c and b + c
• D. a – c and b – c

Answer 1

Answer: (C)

a + c and b + c

Answer 2

x² – (a + b) x + ab + c = 0

α + β = a + b ; αβ = ab + c

Now (x – c – α) (x – c – β) = c

⇒ (x – c)² – (α + β) (x – c) + αβ – c = 0

⇒ (x – c)² – (a + b) (x – c) + ab = 0

⇒ (x – (a + c)) (x– (b + c)) = 0

⇒ x = a + c, b + c