" 9."[p^(2)x^(2)+(p^(2)-q^(2))x-q^(2)=0" (Ans."q^(2)],[-1)]

if x=(sqrt(p^(2)+q^(2))+sqrt(p^(2)-q^(2)))/(sqrt(p^(2)+q^(2))-sqrt(p^(2)-q^(2))), then q^(2)x^(2)-2p^(2)x+q^(2)=?

If x=(sqrt(p^(6)+q^(2))+sqrt(p^(2)-q^(2)))/(sqrt(p^(2)+q^(2))-sqrt(p^(2)-q^(2))) then q^(2)x^(2)-2p^(2)x+q^(2)=?

Solve the x by quadratic formula P^(2)x^(2)+(p^(2)-q^(2))x-q^(2)=0

If the difference of the roots of x^(2)-px+q=0 is unity,then p^(2)+4q=1b .p^(2)-4q=1c*p^(2)+4q^(2)=(1+2q)^(2)d4p^(2)+q^(2)=(1+2p)^(2)

If Sin^(-1)(2p)/(1+p^(2)) - Cos^(-1)((1-q^(2))/(1+q^(2))) = Tan^(-1) (2x)/(1-x^(2)) , then prove that x = (p-q)/(1+pq)

If sec alpha and cosec alpha are the roots of the equation x^(2)-px+q=0 , then a) p^(2)=p+2q b) q^(2)=p+2q c) p^(2)=q(q+2) d) q^(2)=p(p+2)

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))

If the equation 2x^(2)-3xy-py^(2)+x+qy-1=0backslash(p,q in I) represents two mutually perpendicular lines, then (A) p^(2)+q^(2)=13 (B) p-q=5(C)p^(2)-q^(2)=1(D)p+q=5

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 each pair ofthe following three equations x: x^(2)+p_(1)x+q_(1)=0.x^(2)+p_(2)x+q_(2)=0x^(2)+p_(3)x+q_(3)=0, has exactly one root common, prove that (p_(1)+p_(2)+p_(3))^(2)=4(p_(1)p_(2)+p_(2)p_(3)+p_(3)p_(1)-q_(1)-q_(2)-q_(3)]