Multiple choice

If $\alpha$ is a root of reciprocal equation of $ f(x) = 0$ , then the following is also a root of $f(x) = 0$

  1. $-\alpha$
  2. $\alpha^{2}$
  3. $\displaystyle \frac{1}{\alpha}$
  4. $ 2\alpha$
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C Correct answer
Explanation

A reciprocal equation is defined by the property that if x is a root, then 1/x is also a root. This is a standard definition in algebra for equations where the coefficients are symmetric or follow the reciprocal property.

AI explanation

The reciprocal equation of f(x) = 0 is formed by replacing x with 1/x. Therefore, if alpha is a root of the reciprocal equation, substituting alpha for x gives f(1/alpha) = 0. This means 1/alpha must be a root of the original equation f(x) = 0.

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