If `alpha,beta` are roots of `x^2+p x+1=0a n dgamma,delta` are the roots of `x^2+q x+1=0` , then prove that `q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta)` .

If alpha and beta are the roots of x^(2) +px+q=0 and gamma, delta are the roots of x^(2)+rx+s=0, then evaluate (alpha-gamma)(beta-gamma) (alpha-delta) (beta-deta) in terma of p,q, r and s.

If alpha and beta are the roots of x^(2) +px+q=0 and gamma , delta are the roots of x^(2) +rx+x=0 , then evaluate (alpha - gamma ) ( beta - gamma ) (alpha - delta ) ( beta - delta) in terms of p,q,r and s .

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 x^(2)+ax-b=0 and gamma,delta are the roots of x^(2)+ax+b=0 then (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)=

If alpha,beta are the roots of x^(2)+px+q=0and gamma,delta are the roots of x^(2)+px+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= a.1b.q c.r d.q+r

if alpha,beta the roots x^(2)+x+2=0 and gamma,delta the roots of x^(2)+3x+4=0 then find the value of (alpha+gamma)(alpha+delta)(beta+gamma)(beta+delta)