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Question

If a, b, c are real and x33b2x+2c3 is divisible by xa and xb, then


A

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B

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C

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D

a=b=c , a=2b=2c

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Solution

The correct option is C


As f(x)=x33b2x+2c3 is divisible by xa and xb, therefore

f(a)=0a33b2a+2c3=0 ......(i)

and f(b) = 0 ⇒ b33b3+2c3=0 .... (ii)

From (ii), b = c

From (i), a33ab2+2b3=0 (putting b = c)

(ab)(a2+ab2b2)=0

⇒ a = b = c or a2+ab=2b2 and b = c

a2+ab2b2

and b = c is equivalent to a= -2b = -2c


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