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, 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 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)

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 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 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 are the roots of the equationn x^(2)-3x+5=0 and gamma, delta are the roots of the equation x^(2)+5x-3=0 , then the equation whose roots are alpha gamma+beta delta and alpha delta+beta gamma is

If alpha, beta are the roots of the equationn x^(2)-3x+5=0 and gamma, delta are the roots of the equation x^(2)+5x-3=0 , then the equation whose roots are alpha gamma+beta delta and alpha delta+beta gamma is

If alpha, beta are the roots of the equationn x^(2)-3x+5=0 and gamma, delta are the roots of the equation x^(2)+5x-3=0 , then the equation whose roots are alpha gamma+beta delta and alpha delta+beta gamma is