If one roots of the equation is reciprocal of the other, then which one of the following is correct?

A) a = b

B) b = c

C) ac = 1

D) a = c

Correct answer:
D) a = c

Description for Correct answer:

Given quadratic equation is

\( \Large \frac{x^{2}}{a} + \frac{x}{b} + \frac{1}{c} = 0 \) ...(i)

Now, by condition the roots of the Eq. (i)

are \( \Large \alpha \  and \  \frac{1}{ \alpha } \)

Now, product of roots = \( \Large \frac{1/c}{1/a} \)

= \( \Large \alpha .\frac{1}{ \alpha } = \frac{a}{c} \)

= c = a

which is the required relation



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