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Question

The determinant Δ= ∣ ∣ ∣a2+xabacabb2+xbcacbcc2+x∣ ∣ ∣ is divisible by

A
x
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B
x2
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C
x3
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D
None of these
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Solution

The correct options are
A x
B x2

=∣ ∣ ∣a2+xabacabb2+xbcacbcc2+x∣ ∣ ∣

(a2+x)(b2c2+b2x+c2x+x2bx2)ab(abc2+ab2ab2)+ac(ab2cacb2acx)

a2x2+b2x2+c2x2+x3

(a2+b2+c2)x2+x3

x2(a2+b2+c2+x)

Determinant is divisible by x2

also divisible by x.


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