Add:`p(p-q),q(q-r) and r(r-p)`

Divide as directed: 52pqr(p+q)(q+r)(r+p):-104pq(q+r)(r+p)

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(q-p)c = 0

(i) Give examples of polynomials p(x), g(x), q(x) and r(x) , which satisfy the division algorithm and deg p(x)=deg q(x) (ii) Give examples of polynomials p(x), g(x), q(x) and r(x) , which satisfy the division algorithm and deg q(x)=deg r(x) (iii) Give examples of polynomials p(x), g(x), q(x) and r(x) , which satisfy the division algorithm and deg r(x)=0

If a, b, c respectively the p^(th), q^(th) and r^(th) elements of a G.P, thenlebrge Delta = [[loga, logb,logc],[p,q,r],[1,1,1]] equals

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

Let V(r) denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1). Let T(r)=V(r+1)-V(r)-2 and Q(r) =T(r+1)-T(r) for r=1,2 Which one of the following is a correct statement? (A) Q_1, Q_2, Q_3………….., are in A.P. with common difference 5 (B) Q_1, Q_2, Q_3………….., are in A.P. with common difference 6 (C) Q_1, Q_2, Q_3………….., are in A.P. with common difference 11 (D) Q_1=Q_2=Q_3

Prove that |(x,p,q),(p,x,q),(p,q,x)| = (x - p)(x - q)(x + p +q)

If, p,q,r are negative distinct real numbers , then the determinant Delta=|(p,q,r),(q,r,p),(r,p,q)| is :

The roots of the equation (q- r) x^(2) + (r - p) x + (p - q)= 0 are