[" A-8.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 "],[qquad 16q+(r+4-q)^(2)=4p^(2).]

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', 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 roots of the equation (3x+2)^(2)+p(3x+2)+q=0 then roots of x^(2)+px+q=0 are

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

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)