If `alphaa n dbeta` are the roots of `x^2+p x+q=0a n dalpha^4,beta^4` are the roots of `x^2-r x+s=0` , then the equation `x^2-4q x+2q^2-r=0` has always. one positive and one negative root two positive roots two negative roots cannot say anything

If alpha and beta are the roots of x^(2)+px+q=0and 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.A.one positive and one negative root B.two positive roots C.two negative root B.cannot say anything

If alpha and beta are the ral 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 (alpha ne beta, p ne 0 , p,q, r, s in R) :

If alpha,beta are the roots of x^2+2x-4=0 and 1/alpha,1/beta are roots of x^2+qx+r=0 then value of -3/(q+r) is

Find p in R for which x^2-px+p+3=0 has one positive and one negative root.

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 and beta are the roots of the equation x^(2)+ax+b=0 and alpha^(4) and beta^(4) are the roots of the equation x^(2)-px+q=0 then the roots of x^(2)-4bx+2b^(2)-p=0 are always