Chapter 1.2, Problem 23E

Solution

To describe: The error in a given statement and correct it.

The given statement is incorrect. The correct statement is - the intercepts of the graph of the function $y\left(x\right)=5\left(x-2\right)\left(x+3\right)$ are 2 and -3

Given data: The erroneous statement is- the intercepts of the graph of the function $y=5\left(x-2\right)\left(x+3\right)$ are -2 and -3.

Description:

The statement the intercepts of the graph of the function $y\left(x\right)=5\left(x-2\right)\left(x+3\right)$ are -2 and -3 is incorrect.

Explanation:

The intercepts of a curve on the x -axis are the values of x obtained by solving equation $y\left(x\right)=0$ .

The solution of equation $y\left(x\right)=0$ is given by,

  $\begin{array}{c}5\left(x-2\right)\left(x+3\right)=0\\ \left(x-2\right)=0\Rightarrow x=2\\ \left(x+3\right)=0\Rightarrow x=-3\end{array}$

Therefore, the intercepts of the graph of the function on the x-axis are $x=2$ and $x=-3$ .

But stated intercepts are -2 and -3.Hence, the given statement is incorrect.

The correct statement is - the intercepts of the graph of the function $y\left(x\right)=5\left(x-2\right)\left(x+3\right)$ are 2 and -3