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Question

If a,b,c are different real numbers and x is a variable then a factor of the determinant

∣∣ ∣ ∣∣0x2−ax3−bx2+a0x2+cx4+bx−c0∣∣ ∣ ∣∣ is


A

x

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B

xa

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C

xb

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D

x+a

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Solution

The correct option is A

x


Here if we closely observe that a,b and c are in opposite signs on opposite sides of the diagonal.

So if we put x=0 the determinant becomes something like this

∣ ∣0aba0cbc0∣ ∣, which is the determinant of a skew symmetric matrix. We know that the determinant of a skew symmetric matrix is 0.

So if we put x=0 in the determinant then the value of determinant becomes zero. So x0 is a factor of the above mentioned determinant which is the correct answer.


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