Step-by-Step Solution
Key Concept: $p^2 x^2 + p^2 x - q^2 x - q^2 = 0 \Rightarrow p^2 x(x + 1) - q^2(x + 1) = 0 \Rightarrow (p^2 x - q^2)(x + 1) = 0 \Rightarrow x = q^2/p^2$ or $x = -1$.
$p^2 x^2 + p^2 x - q^2 x - q^2 = 0$. [1.5 Marks]
$p^2 x(x + 1) - q^2(x + 1) = 0 \Rightarrow (p^2 x - q^2)(x + 1) = 0$. [2.0 Marks]
$x = \dfrac{q^2}{p^2}$ or $x = -1$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Splitting middle term: 1.5 Marks
Factoring into $(p^2 x - q^2)(x + 1) = 0$: 2.0 Marks
Finding roots $q^2/p^2$ and $-1$: 1.5 Marks
Correct Answer: