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Question
If a and b are roots of the equation \[x^2 - px + q = 0\], than write the value of \[\frac{1}{a} + \frac{1}{b}\].
Solution
Given:
\[x^2 - px + q = 0\]
Also,
\[a\] and \[b\] are the roots of the given equation.
Sum of the roots = \[a + b = p\] ...(1)
Product of the roots = \[ab = q\] ...(2)
Now,
\[\frac{1}{a} + \frac{1}{b} = \frac{b + a}{ab} = \frac{p}{q}\]
[Using equation (1) and (2)]
Hence, the value of \[\frac{1}{a} + \frac{1}{b}\] is \[\frac{p}{q} .\]
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