Explain why #x^3-3x+8=0# has only one real root?

1 Answer
Mark D.
Apr 17, 2018

See below

Explanation:

A cubic can have 1,2 or 3 roots. In general terms they rise up from bottom left have a point of inflection or a maximum and minimum then continue to rise up to the right. If the point of inflection or the max and min occur below or above the X axis you only get one root as the graph crosses the axis only once. If the max is above and the min below you can have three roots. If you have a repeated root then you get only two roots.

This graph crosses the X axis at (-2.5,0) has a max at (-1,10) crosses the y axis at (0,8) then a min at (1,6) then rises up and away. Sorry don't know how to draw on here! Maybe another contributor can pull in a picture.

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