If $α$ and $β$ are the zeros of the polynomial $f (x) = 5 x^{2} - 7 x + 1$ , find the value of $(\frac{1}{α} + \frac{1}{β}) .$ .

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Solution

We have to find

$(\frac{1}{α} + \frac{1}{β})$

Now $(\frac{1}{α} + \frac{1}{β}) = \frac{α + β}{α β}$ (taking LCM)

Now by the given polynomial.

$f (x) = 5 x^{2} - 7 x + 1$

we get,

$(α + β) = \frac{- b}{a} = \frac{7}{5}$

$α β = \frac{c}{a} = \frac{1}{5}$

so, $\frac{α + β}{α β} = \frac{(\frac{7}{5})}{(\frac{1}{5})}$

$= \frac{7}{1} = 7$

So, $(\frac{1}{α} + \frac{1}{β}) = \frac{α + β}{α β} = 7$

Hence, $(\frac{1}{α} + \frac{1}{β}) = 7$

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