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How to use mathematics in root piercing?
There is a saying: from top to bottom, from right to left, I don't wear strange clothes "(you can also remember:" from top to bottom, from right to left, I occasionally wear strange clothes "or" I even wear strange clothes ").

Specific as follows

first step

Through many properties of inequality, the inequality is shifted so that the right side is 0. (Note: Make sure that the coefficient before x is positive. )

Such as x3-2x2-x+2 >; 0 to (x-2)(x- 1)(x+ 1)>0.

Second step

Solve all roots with equal sign instead of unequal sign.

For example, the root of (x-2)(x- 1)(x+ 1)=0 is: x 1=2, x2= 1, x3=- 1.

Third step

Mark each root in turn from left to right on the number axis.

For example:-1 1 2

Fourth step

Draw a line through the root: based on the number axis, from the upper right of the rightmost root through the root, to the lower left, and then through the second right root, one by one through the root.

Step five

Observe the inequality, and if the inequality is ">", take the range above the number axis and within the root line; If the inequality symbol is "

For example:

The root of if (x-2) (x-1) (x+1) > 0.

Mark root on the number axis:-1 1 2

Draw a line: cross the root from the top right.

Because the symbol of inequality is ">", the range above the number axis and within the root line is taken. Namely:-1