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Question

If ∣ ∣x+22x+33x+42x+33x+44x+53x+55x+810x+17∣ ∣=0


then find value of x

A
1
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B
2
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C
-1
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D
-2
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Solution

The correct options are
C -1
D -2
Let Δ=∣ ∣x+22x+33x+42x+33x+44x+53x+55x+810x+17∣ ∣

Applying R2R2R1,R3R3R1

Δ=∣ ∣x+22x+33x+4x+1x+1x+12x+33x+57x+13∣ ∣=(x+1)∣ ∣x+22x+33x+41112x+33x+57x+13∣ ∣

Again applying C2C2C1,C3C3C1

Δ=(x+1)∣ ∣x+2x+12x+21002x+3x+25x+10∣ ∣

=(x+1)((x+1)(5x+10)(x+2)(2x+2))

=(x+1)2(5x+102x4)=(x+1)2(3x+6)

For Δ=0x=1,x=2

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