# f(x) = x^3 - 3x^2 + 3 has no rational roots.  Use the graphing calculator to approximate the irrational solutions correct to 3 decimals. If there is more than 1 Real solution, enter them from...

f(x) = x^3 - 3x^2 + 3 has no rational roots.  Use the graphing calculator to approximate the irrational solutions correct to 3 decimals.

If there is more than 1 Real solution, enter them from smallest to largest.

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

First graph the function to estimate the zeros:

There are three real roots -- one between -1 and zero, one between 1 and 2, and the last between 2 and 3.

Using a graphing calculator the approximations are:

`x~~-.8793852,x~~1.3472964,x~~2.5320889`

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To 3 decimal places, the approximations for the real roots are x=-.879,x=1.347, and x=2.532

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If you do not have a graphing calculator, there are good emulators available. You might try gcalc (you might need Java enabled for full functionality.)

Another thing you can do is to use geogebra. You can run this online or download a free version.