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

If alpha , beta are the roots of x^2 + px +1=0 and gamma , delta are the roots of x^2 +qx +1=0 then (alpha - gamma )(beta - gamma)(alpha + delta )( 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 roots of x^(2)+-px+1=0 and gamma,delta are the roots of x^(2)+qx+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) + qx + 1 = 0 and gamma, delta the roots of x^(2) + qx + 1 = 0 , then the value of (alpha - gamma ) (beta - gamma ) (a + delta ) beta + delta) is :

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 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) .