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Existence of Limit

If a and b ar...

Question

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

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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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