# Graphical solutions to x^3 - 8x + 1 = 1

• September 14th 2010, 12:08 PM
blfan
Graphical solutions to x^3 - 8x + 1 = 1
use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. all solutions lie between -10 and 10
x^3 - 8x + 1 = 1
• September 14th 2010, 12:13 PM
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Quote:

Originally Posted by blfan
use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. all solutions lie between -10 and 10
x^3 - 8x + 1 = 1

What kind of calculator do you have? You can either graph y = x^3 - 8x + 1 and y = 1 simultaneously and find intersection points, or graph y = x^3 - 8x and find roots.
• September 14th 2010, 12:20 PM
e^(i*pi)
Quote:

Originally Posted by blfan
use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. all solutions lie between -10 and 10
x^3 - 8x + 1 = 1

This one isn't too hard to solve algebraically but nonetheless put the graph of $x^3-8x=0$ and look for y intercepts which will be the roots of the equation.

Algebra gives solutions of $0, 2\sqrt{2}, -2\sqrt{2}$

See attached graph (done in kmplot) Attachment 18921