Question

What is the zero of p(x) = ax-b

Answer 1

The zero of a function is the value of x (independent variable) where the value of f(x) (dependent variable) equals zero.

Thus,

$\text{when f(x)=0, x is a zero of the function}$

Given:

$p(x)=ax-b$

the zero of p(x) is the value of x where p(x) equals zero.

Thus,

$\begin{gathered} p(x)=ax-b=0 \\ \Rightarrow ax-b=0 \\ \text{Add b to both sides of the equation} \\ ax-b+b=0+b \\ ax=b \\ \text{divide both sides of the equation by the coefficient of x.} \\ \text{the }coefficient\text{ of x is a} \\ \text{thus,} \\ \frac{ax}{a}=\frac{b}{a} \\ \Rightarrow x=\frac{b}{a} \end{gathered}$

Hence, the zero of the p(x) function is

$\frac{b}{a}$