Solve $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

- 1, p^{2} q^{2}

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1, \frac{p^{2}}{q^{2}}

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- 1, \frac{q}{p}

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- 1, \frac{q^{2}}{p^{2}}

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Solution

The correct option is C $- 1, \frac{q^{2}}{p^{2}}$
Rewrite, $p^{2} + p^{2} x - q^{2} x - q^{2} = 0$
$\Rightarrow$ $p^{2} x (x + 1) - q^{2} (x + 1) = 0$
$\Rightarrow$ $(x + 1) (p^{2} x - q^{2}) = 0$
$\Rightarrow$ If $x - 1 = 0$ or $(p^{2} x - q^{2})$ =0
$\Rightarrow$ $x = - 1$ or $x = \frac{q^{2}}{p^{2}}$

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