Chapter 7.8, Problem 29E

To determine

To calculate:The $x-\mathrm{coordinates}$ of the points where the graph crosses the $x-axis$ .

Answer to Problem 29E

The $x-\mathrm{coordinates}$ of the points where the graph crosses the $x-axis$ are $x=-9,0,9$ .

Explanation of Solution

Given information:A graph is given whose equation is $y=x^3-81x$ .

Calculation:

To find the $x-\mathrm{intercept}$ , putting $y=0$ in given equation,

  $x^3-81x=0$

  $\Rightarrow x(x^2-81)=0$ (Factoring out $x$ )

  $\Rightarrow x(x^2-9^2)=0$

  $\Rightarrow x(x+9)(x-9)=0$

  $\Rightarrow x=0$ $or$ $x+9=0$ $or$ $x-9=0$

  $\Rightarrow x=0$ $or$ $x=-9$ $or$ $x=9$

Thus, the $x-\mathrm{coordinates}$ of the points where the graph crosses the $x-axis$ are $x=-9,0,9$ .