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).`

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

Let alpha and beta be the roots of the equation ax^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-ac)=a^2(B^2-AC) .

If alpha , beta are the roots of ax ^2+2bx +c=0 and alpha + sigma , beta + sigma are the roots of Ax^2 + 2Bx +c=0 then (b^2-ac)/(B^2-AC)=

If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and 3b^2=16ac then

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, gamma are the roots of the equation x^(3) - ax^(2) + bx -c = 0 , then sum alpha^(2) (beta + gamma)=

If alpha , beta , gamma are roots of the equation x^3 + ax^2 + bx +c=0 then alpha^(-1) + beta^(-1) + gamma^(-1) =

If alpha , beta , gamma are roots of the equation x^3 + ax^2 + bx +c=0 then alpha^(-1) + beta^(-1) + gamma^(-1) =

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)) .