If the roots of `ax^(2) + bx + c` are `alpha,beta` and the roots of `Ax^(2) + Bx + C=0` are `alpha- K,beta-K`, then `(B^(2) - 4AC)/(b^(2) - 4ac)` is equal to -

Options

A. 0
B. 1
C. `((A)/(a))^(2)`
D. `((a)/(A))^(2)`

Answer

3

Explanation

`|alpha-beta| = |(alpha-K)-(beta -K)|`
`sqrt(D_(1))/(|a|)=sqrt(D_(2))/(|A|)`
`rArr (D_(1))/(D_(2)) =(a^(2))/(A^(2))`
`rArr (B^(2)-4Ac)/(b^(2) - 4ac) =(D_(2))/(D_(1)) = (A^(2))/(a^(2))`