If `2 + cos^2 alpha, 2 + sin^2 alpha` are the roots of `x^2 + 2bx + c=0 and 4+cos^4 alpha,4+sin^4 alpha` are the roots of `x^2 + 2qx +r = 0` then

If alpha, beta are the roots of x^(2) + bx + c = 0 and, alpha +h, beta+h are the roots of x^(2) + qx +r = 0 then h =

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 :

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

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

If alpha. beta are the roots of x^2 +bx+c=0 and alpha + h, beta + h are the roots of x^2 + qx +r=0 then 2h=