If a and b are roots of the equation x


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


Given: $x^{2}-p x+q=0$

Also, $a$ and $b$ are the roots of the given equation.

Sum of the roots $=a+b=p$    ...(1)

Product of the roots $=a b=q$   .....(2)

Now, $\frac{1}{a}+\frac{1}{b}=\frac{b+a}{a b}=\frac{p}{q}$    [Using equation (1) and (2)]

Hence, the value of $\frac{1}{a}+\frac{1}{b}$ is $\frac{p}{q}$.

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