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If α,β are roots of the equation (x–a)(x–b)+c = 0 (c  0), then then 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)  None of these 

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Correct option   (c) a+c and b+c

Explanation:

x– (a + b)x + ab + c = 0

α + β = a + b and α β = ab + c

Now (x – c – α)(x – c – β ) = c

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

(x – c)– (a + b)(x – c) + ab = 0

(x – c)2– a(x – c) – b(x – c) + ab = 0

⇒ (x – c – a)(x – c – b) = 0

x = c + a and b + c 

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