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 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. A. one positive and one negative root B . two positive roots C . two negative roots D . 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 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 A. Can t say anything B. two positive roots C. two negative roots D. one positive and one negative root

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

If p and q are the roots of x^2 + px + q = 0 , then find p.

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e nh= -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/q-q/p) d. none of these

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

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) .

If one root of x^(2) + px+12 = 0 is 4, while the equation x ^(2) + px + q = 0 has equal roots, then the value of q is

If alpha,beta are the roots of the equation x^2+p x+q=0,t h e n-1/alpha,-1/beta are the roots of the equation (a) x^2-p x+q=0 (b) x^2+p x+q=0 (c) q x^2+p x+1=0 (d) q x^2-p x+1=0