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

Options

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)`

Answer

B

Explanation

`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)`