First slide

Theory of equations

Question

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

Moderate

A

$\frac{1}{p}$
B

$\frac{1}{q}$
C

$\frac{1}{2 p}$
D

$\frac{p}{q}$

Solution

Roots of given equation $x^{2} - px + q = 0$ is a and b i.e.,
$a + b = p . . . (i) and ab = q . . . (ii)$
Then $\frac{1}{a} + \frac{1}{b} = \frac{(a + b)}{ab} = \frac{p}{q}$ .

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