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" If " Delta(1) =|{:(x,,b,,b),(a,,x,,b)...

`" If " Delta_(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta_(2)= |{:(x,,b),(a,,x):}|` are the given determinants then

A

`Delta_(1)=3(Delta_(2))^(2)`

B

`(d)/(dx) (Delta_(1)) =3Delta_(2)`

C

`(d)/(dx) (Delta_(1)) =3(Delta_(2))^(2)`

D

`Delta_(1)=3Delta_(2)^(3//2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Delta_(1)=x(x^(2) -ab)-b(ax-ab)+b(a^(2)-ax)`
`=x^(3) -3abx +ab^(2) +a^(2)b`
`(d)/(dx) (Delta _(1))=3x^(2) -3ab=3(x^(2) -ab)=3Delta_(2)`
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