If a and b are roots of x 2 - p x + q = 0 , then 1 a + 1 b =

Question

If $a$ and $b$ are roots of $x^{2} - p x + q = 0$ , then $\frac{1}{a} + \frac{1}{b} =$

Smart Achievers · Accepted Answer

(4)

$Given a, b are roots of x^{2} - p x + q = 0$

$∴$ $Sum, a + b = p,$ $product, a b = q$

$\frac{p}{q} = \frac{sum of roots}{product of roots} = \frac{a + b}{a b} = \frac{1}{a} + \frac{1}{b}$

$∴$ $\frac{p}{q} = \frac{1}{a} + \frac{1}{b}$

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