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Question

If Δ=∣ ∣x22x33x42x33x44x53x55x810x17∣ ∣=Ax3+Bx2+Cx+D, then B+C is equal to

A
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B
1
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C
3
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D
9
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Solution

The correct option is C 3
Given:
Δ=∣ ∣x22x33x42x33x44x53x55x810x17∣ ∣

R2R2R1, R3R3R2

Δ=∣ ∣x22x33x4x1x1x1x22(x2)6(x2)∣ ∣

Δ=(x1)(x2)∣ ∣x22x33x4111126∣ ∣

C2C2C1, C3C3C1

Δ=(x1)(x2)∣ ∣x2x12x2100115∣ ∣

Δ=(x1)(x2){(5(x1)+(2x2)}

Δ=(x1)(x2)(3x+3)

Δ=3(x1)2 (x2)

Δ=3x3+12x215x+6

Also, Δ=Ax3+Bx2+Cx+D
comparing the coefficient of same powers
A=3, B=12, C=15
B+C=1215=3

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