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Question

If a,b,c are in A.P, then ∣∣ ∣∣x+1x+2x+ax+2x+3x+bx+3x+4x+c∣∣ ∣∣ equals

A
a+b+c
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B
x+a+b+c
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C
0
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D
None of these
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Solution

The correct option is C 0
Since a,.b,c in AP, so 2b=a+c
∣ ∣x+1x+2x+ax+2x+3x+bx+3x+4x+c∣ ∣
R22R2R1R3
∣ ∣x+1x+2x+a002b(a+c)x+3x+4x+c∣ ∣
∣ ∣x+1x+2x+a000x+3x+4x+c∣ ∣=0 (2b=a+c)

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