If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} + x - 2$ , find the value of $\frac{1}{α} - \frac{1}{β}$

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$\begin{matrix} f (x) = x^{2} + x - 2 \Rightarrow s u m o f r o o t s = α + β = - 1 \Rightarrow p r o d u c t o f r o o t s = α - β = - 2.... (1) ∴ v a l u e o f \frac{1}{α} - \frac{1}{β} = \frac{β - α}{α β} = \frac{- (α - β)}{α β} . . . . (2) \Rightarrow α - β = \frac{\sqrt{D}}{a} = \frac{\sqrt{b^{2} - 4 a c}}{a} = \frac{\sqrt{1 + 4 \times 2 \times 1}}{1} = 3 α - β = 3.... (3) p u t t i n g t h e v a l u e o f α β a n d α - β i n e q u a t i o n (2) \Rightarrow \frac{1}{α} - \frac{1}{β} = \frac{- (3)}{- 2} = \frac{3}{2} \end{matrix}$

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