If `alpha and beta` are roots of `x^2 + 21x + 4 = 0 and sqrt alpha/beta,sqrt beta/alpha `,are roots of `px^2+qx+2=0` then value of `alpha(26p+q)` 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 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 a ^2 x + bx +c=0 and alpha + h+ beta + h are the roots of px^2+qx +r=0 then h=

If alpha and beta are roots of the equation qx^2+px+p=0 ,show that sqrt(alpha/beta)+sqrt(beta/alpha)+sqrt(p/q)=0

If alpha and beta are the roots of the equation px^(2) + qx + 1 = , find alpha^(2) beta + beta^(2)alpha .

If alpha and beta are roots of x^2+px+2=0 and 1/alpha,1/beta are the roots of 2x^2+2qx+1=0 . Find the value of (alpha-1/alpha)(beta-1/beta)(alpha+1/beta)(beta+1/alpha)

If alpha and beta are roots of x^2+px+2=0 and 1/alpha,1/beta are the roots of 2x^2+2qx+1=0 . Find the value of (alpha-1/alpha)(beta-1/beta)(alpha+1/beta)(beta+1/alpha)1

If alpha, beta,gamma are roots of x^(3) - px^(2) + qx - r = 0 then sum alpha (beta + gamma) =