Question

If $b$ is a root of a reciprocal equation, $f\left(x\right)=0$, then another root of $f\left(x\right)=0$ is:

• A. $\frac{-1}{b}$
• B. $\frac{1}{b^2}$
• C. $\sqrt{b}$
• D. $\frac{1}{b}$

Answer 1

The correct option is D $\frac{1}{b}$

A reciprocal equation is an equation whose roots can be divided into pairs of numbers, each the reciprocal of the other.

(equivalently) an equation which is unchanged if the variable $x$ is replaced by its reciprocal $\frac{1}{x}$ is reciprocal equation.

Since one root is $b$, then the other root is $\frac{1}{b}$

Hence, option D is correct.