[" If "alpha,beta" and "gamma,delta" are the roots of the equations "x^(2)-bx+c=0],[" and "x^(2)-px+q=0quad " respectively,show that,"],[(alpha-gamma)(beta-delta)+(beta-gamma)(alpha-delta)=2(c+q)-bp]

IF alpha,beta and gamma, delta are the roots of the equations x^2-bx+c=0 and x^2-px+q=0 respectively, show that , (alpha-gamma)(beta-delta) -alpha.gamma - beta. delta=(c+q)-bp .

IF alpha,beta and gamma,delta be the roots of the equation x^2+px-r=0 and x^2+px+r=0 respectively, prove that (alpha-gamma)(alpha-delta)=(beta-gamma)(beta-delta)

If alpha,beta are the roots of the equation x^(2)+px+1=0 gamma,delta the roots of the equation x^(2)+qx+1=0 then (alpha-gamma)(alpha+delta)(beta-gamma)(beta+delta)=

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

If alpha and beta are the roots of the equation x^(2) +px+1=0 , gamam , delta are the roots of (x^(2) +qx+1=0 , then , find ( alpha-gamma ) (beta - gamma ) ( alpha + delta )(beta + delta )

If alpha, beta and gamma are the roots of the equation x^(3) + px + q = 0 (with p != 0 and p != 0 and q != 0 ), the value of the determinant |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is

If alpha, beta and gamma are the roots of the equation x^(3) + px + q = 0 (with p != 0 and p != 0 and q != 0 ), the value of the determinant |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is

If alpha,beta,gamma and delta are roots of equation x^(4)-7x^(2)+x-5=0, then the value of (alpha+beta+gamma)(alpha+beta+delta)(beta+gamma+delta)(alpha+gamma+delta) is equal to

If alpha and beta are the roots of quadratic equation x^(2)+px+q=0 and gamma and delta are the roots of x^(2)+px-r=0 then (alpha-gamma)(alpha-delta)