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If alpha and beta are the roots of the e...

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

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))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(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))`
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