Question

How do I use graphing calculator to find the real zeros of \[f\left( x \right)={{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\]

Answer 1

Hint: In order to find the real zeros of this equation of the given function \[f\left( x \right)={{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\] with the help of graphing TI-83/84 calculator. First turn on the calculator then press the top-leftmost button “Y=” on that calculator there you’ll find several options to plot and write the function. In the first attribute write the right side of the given function that is \[{{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\] then press the “graph” button which you’ll find on the right side of the calculator then graph of this function will be shown plotted. To find real zeros remember that the meaning of real zeros of the function is the points at which the curve of the function is cutting the x-axis. Determine those points by observing the graph and with the help of “calc menu” then you’ll get your required answer.

Complete step by step solution:
Given function is as follows:
\[f\left( x \right)={{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\]
In order to find the real zeros of this equation of the given function with the help of graphing TI-83/84 calculator. Follow the following steps.
1.Turn on your calculator.
2.Press the left most top button on that calculator there you’ll find several options to plot and write the functions to plot.
3.In the first attribute write the right side of the given function that is \[{{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\] which is actually going to be written in this form “\[x\hat{\ }4+x\hat{\ }3-11x\hat{\ }2-9x+18\] “ with the help of keys in the calculator.
4.Now press the “graph” button which you’ll find on the right side of the calculator then the graph of this function will be shown plotted.
5.To find real zeros remember that the meaning of real zeros of the function is the points at which the curve of the function is cutting the x-axis.
6.To Determine those points and the location of these points on the graph, press the “2nd+trace” button to get the “calc” menu. And select “zero” from the options.
7.Now the graph screen will be visible to you with a cursor. Move this cursor with the help of up-down, right-left buttons at press okay on the point at which it’s cutting the x-axis. 8.Location of that point will be visible to you and you can write it down.
9.Repeat steps 6 and 7 until you determine the location of all the points cutting the x-axis that is the real zeroes.
10.In this question you will get \[x=-3,-2,1,3\]
Therefore, real zeros of the function \[f\left( x \right)={{x}^{4}}+{{x}^{3}}-11{{x}^{2}}-9x+18\] are \[x=-3,-2,1,3\].

Note:
Students can go wrong by skipping the “calc” step and determining the zeros by just observing the graph which can lead to the wrong answer because it’ll not give an accurate answer in all the cases.