If the roots of the equation 1x+p+1x+q=1rare equal in magnitude but opposite in sign, then the product of the roots will be

Given equation 1x+p+1x+q=1rcan be rewritten asx2+x(p+q−2r)+pq−pr−qr=0……………………….(i)Let roots are α and - α, then the product of roots−α2=pq−pr−qr=pq−r(p+q)………………………(ii)and            sum of roots, 0=−(p+q−2r)⇒                          r=p+q2……………………….(iii)On solving Eqs. (ii) and (iii), we get−α2=pq−p+q2(p+q)=−12(p+q)2−2pq⇒ α2=−p2+q22