If the  roofs of the  equation  1x+p+1x+q=1rare equal in magnitude and opposite' in sign, then the product of root,  is

The equation 1x+p+1x+q=1r or  x2+(p+q−2r)x−r(p+q)+pq=0 Let α,β  be the roots of this equation. Then, α+β=−(p+q−2r)  and  αβ=−r(p+q)+pqIt is given that α+β=0. Therefore, , p+q=2r ∴ αβ=−r(p+q)+pq=−12(p+q)2+pq=−12p2+q2