Question

If a and b are roots of the equation \[x^2 - px + q = 0\], than write the value of \[\frac{1}{a} + \frac{1}{b}\].

Answer 1

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  \[\frac{p}{q} .\]