If $\alpha, \beta$ are zeroes of $x^2 + x - 2$, find the value of $\dfrac{1}{\alpha} - \dfrac{1}{\beta}$.
Step-by-Step Solution
Key Concept: $x^2 + x - 2 = (x + 2)(x - 1) = 0 \Rightarrow \alpha = 1, \beta = -2$ or vice versa.
Zeroes are $1$ and $-2$. [1.0 Mark]
If $\alpha = 1, \beta = -2 \Rightarrow \dfrac{1}{1} - \dfrac{1}{-2} = 1 + 1/2 = 3/2$.
If $\alpha = -2, \beta = 1 \Rightarrow -1/2 - 1 = -3/2$.
Value is $\pm \dfrac{3}{2}$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Finding zeroes $1, -2$: 1.0 Mark
Evaluating $\pm 3/2$: 2.0 Marks
Correct Answer: