If `alpha,beta` are roots of `x^2-px+q=0` and `alpha-2,beta+2` are roots of `x^2-px+r=0` then prove that `16q+ (r+4-q)^2=4p^2`.

If alpha,beta are the roots of x^(2)-px+r=0 and alpha+1,beta-1 are the roots of x^(2)-qx+r=0 ,then r is

IF alpha , beta are the roots of x^2 +px +q=0 and alpha ^4 , beta ^4 are the roots of x ^2 - rx +s=0 then the equation x^2-4qx +2q^2 -r=0 has always

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

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 real roots of x^(2) + px + q= 0 and alpha^(4), beta^(4) are the roots of x^(2) - rx + s = 0 , then the equation x^(2) - 4 q x + 2q^(2) - r = 0 has always