# How do I use a graphing calculator to find the real zeros of y=(x-12)^3-7?

Jan 24, 2016

Only one real root. $x \approx 13.9$

#### Explanation:

We can find out the number of zeros of any polynomial by looking at the points the graph crosses x axis.
The real roots of any polynomial correspond to x-intercept of its graph
For plotting the graph in the calculator we need to express polynomial as below by opening the bracket.

$y = {x}^{3} - 36 {x}^{2} + 432 x - 1735$

Zoomed in graph{y=x^3-36x^2+432x-1735 [-18.17, 17.39, -6.83, 10.95]}

From the graph we see that only one real root exists.
point where the graph crosses the x axis.

We have only one real root, i.e., $x \approx 13.9$