If `alpha,beta` are the roots of `a x^2+b x+c=0,(a!=0)` and `alpha+delta,beta+delta` are the roots of `A x^2+B x+C=0,(A!=0)` for some constant `delta` then prove that (2000, 4M) `(b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)`

If alpha,beta are the roots of ax^(2)+bx+c=0,(a!=0) and alpha+delta,beta+delta are the roots of Ax^(2)+Bx+C=0,(A!=0) for some constant delta then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2))

If alpha , beta are the roots of ax^(2) +bx+c=0, ( a ne 0) and alpha + delta , beta + delta are the roots of Ax^(2) +Bx+C=0,(A ne 0) for some constant delta , then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2)) .

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 and alpha+delta,beta+delta are the roots of the equation Ax^(2)+Bx+C=0 then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2)) for some constant value of delta

If alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta be those of Ax^(2)+2Bx+C=0 then prove that (b^(2)-ac)/(B^(2)-AC)=((a)/(A))^(2)

If alpha,beta are the roots of x^(2)+ax-b=0 and gamma,delta are the roots of x^(2)+ax+b=0 then (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)=

Let alpha and beta be the roots of the equationa x^(2)+2bx+c=0 and alpha+gamma and beta+gamma be the roots of Ax^(2)+2Bx+C=0. Then prove that A^(2)(b^(2)-4ac)=a^(2)(B^(2)-4AC)

If alpha and beta are the roots of the equation 2x^(2)+7x+c=0 and | alpha^(2)-beta^(2)|=(7)/(4) then c=