If the roots of the equation `ax^(2)+bx+c=0(a!=0)` be `alpha` and `beta` and those of the equation `Ax^(2)+Bx+C=0(A!=0)` be `alpha+k` and `beta+k`.Prove that
`(b^(2)-4ac)/(B^(2)-4AC)=(a/A)^(2)`

Explanation

`:'alpha-beta=(alpha+k)-(beta+k)`
`implies(sqrt(b^(2)-4ac))/a=(sqrt((B^(2)-4AC)))/A[ :' alpha-beta=(sqrt(D))/a]`
`impliessqrt(((b^(2)-4ac)/(B^(2)-4AC)))=(a/A)`
On squaring both sides then we get
`(b^(2)-4ac)/(B^(2)-4AC)=(a/A)^(2)`