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