Determine `P` ,so that,the following equation has coincident roots `T^(2)+P^(2)=2(P+1)T`

Find the value of P for which the following equation has equal roots px ^2−8x+2p=0

Determine the nature of roots of the following quadratic equations. (ii) p^2-sqrt(3)p+2=0 .

Determine the nature of roots of the following quadratic equations. (ii) p^2-sqrt(3)p+2=0 .

With the help of fthermondynamic equation of state ((delU)/(delV))_(T)=T((delP)/(delT))_(V)-P Answer the following questions for a van der Waals' gas P=(nRT)/(V-nb)-(an^(2))/V^(2) DeltaH for the insothermal process from (P_(1)V_(1)T) to (P_(2)V_(2)T) to is :

Find P (0),P(1) and P(2) for each of the following polynomials. P(t) = 2 +t +2t^(2)-t^(3)

The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all real. (A) if the equation has one real root then q'^2-pp'q'+qp'^2=0 (B) if the equation has two equal roots then pp'=2q' (C) if the equation has two equal roots then p^2-p'^2=4q (D) if the equation has one real root then p'^2-pp'q'+q'^2=0

Find p(0), p(1) and p(2) for each of the following polynomials : p(t) = 2 + t + 2t^(2) - t^(3)

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)