If `alpha` and `beta` are the roots of the equation `ax^(2)+bx+c=0` then the sum of the roots of the equation `a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0` is

Options

A. `-(alpha^(2)-beta^(2))`
B. `(alpha+beta)^(2)-2alpha beta`
C. `alpha^(2)beta+beta alpha^(2)-4alpha beta`
D. `-(alpha^(2)+beta^(2))`

Answer

D

Explanation

`(d)` `alpha+beta=-(b)/(a)`, `alpha beta=(c )/(a)`,
Sum of roots of the equation `a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0` ,brgt `x_(1)+x_(2)=(2ac-b^(2))/(a^(2))`
`=(2c)/(a)-((b)/(a))^(2)`
`=2alpha beta-(alpha+beta)^(2)`
`=-(alpha^(2)+beta^(2))`