If `Delta_1=|[x, b, b],[ a, x, b],[ a, a, x]|` a n d `Delta_2=|[x, b],[ a, x]|` are the given determinants, then `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=3(Delta_2)^ (3//2)`

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

`(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)`