If roots of the equation `(q-r)x^(2)+(r-p)x+(p-q)=0` are equal then `p,q,r` are in

if the roots of the equation z^(2) + ( p +iq) z + r + is =0 are real wher p,q,r,s, in ,R , then determine s^(2) + q^(2)r .

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

If the roots of the equation 1/(x+p)+1/(x+q)=1/r are equal in magnitude and opposite in sign, then (A) p+q=r (B)p+q=2r (C) product of roots=- 1/2(p^2+q^2) (D) sum of roots=1

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If t_n denotes the nth term of an A.P. and t_p= 1/q, t_q= 1/p then which one of the following is necessarily a root of the equation (p+2q-3r)x^2+(q+2r-3p)x+(r+2p-3q)=0 (A) t_p (B) t_q (C) t_(pq) (D) t_(p+q)