If `beta + cos^2alpha, beta +sin^2alpha` are roots of `x^2 + 2bx + c = 0` and `gamma + cos^4alpha,gamma+sin^4alpha` are the roots of `X^2+2BX+C=0` then prove that `b^2-B^2=c-C`

If beta + cos ^(2) alpha, beta + sin ^(2) alpha are the roots of x ^(2) + 2 bx +c=0 and gamma + cos ^(4) alpha, gamma + sin ^(4) alpha are the roots of x ^(2) + 2Bx+C=0, then :

If beta + cos ^(2) alpha, beta + sin ^(2) alha are the roots of x ^(2) + 2 bx +c=0 and gamma + cos ^(4) alpha, gamma + sin ^(4) alpha are the roots of x ^(2) + 2Bx+C=0, then :

If beta + cos ^(2) alpha, beta + sin ^(2) alha are the roots of x ^(2) + 2 bx +c=0 and gamma + cos ^(4) alpha, gamma + sin ^(4) alpha are the roots of x ^(2) + 2Bx+C=0, then :

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) .

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

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).

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

alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta are the roots of A x^(2)+2Bx+C=0 , then what is (b^(2)-ac)//(B^(2)-AC) equal to ?