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)`

If alpha,beta are the roots of x^(2)+px+q=0and gamma,delta are the roots of x^(2)+rx+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p,q,r, ands.Deduce the condition that the equation has a common root.

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 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 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,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)=