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It is given that $p^2x^2 + (p^2 - q^2)x - q^2 = 0; (p \neq 0)$
(i) Show that the discriminant (D) of above equation is a perfect square.
(ii) Find the roots of the equation.
(i) Show that the discriminant (D) of above equation is a perfect square.
(ii) Find the roots of the equation.
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(i) Discriminant $= (p^2 - q^2)^2 + 4p^2q^2 = (p^2 + q^2)^2$ [$1 + 1$ mark]
(ii) $\therefore x = \frac{-(p^2 - q^2) \pm \sqrt{(p^2 + q^2)^2}}{2p^2}$ [$1$ mark]
$= \frac{q^2}{p^2}, -1$ [$1 + 1$ mark]
(ii) $\therefore x = \frac{-(p^2 - q^2) \pm \sqrt{(p^2 + q^2)^2}}{2p^2}$ [$1$ mark]
$= \frac{q^2}{p^2}, -1$ [$1 + 1$ mark]