Algebra Examples

Find the Bounds of the Zeros
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Simplify each term.
Move to the left of the expression .
Multiply by to get .
Rewrite as .
Simplify .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Create a list of the coefficients of the function except the leading coefficient of .
There will be two bound options, and , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add .
Arrange the terms in ascending order.
The maximum value is the largest value in the arranged data set.
The absolute value is the distance between a number and zero. The distance between and is .
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than , use that number. If not, use .
Simplify each term.
The absolute value is the distance between a number and zero. The distance between and is .
The absolute value is the distance between a number and zero. The distance between and is .
Arrange the terms in ascending order.
The maximum value is the largest value in the arranged data set.
The bound options are the same.
Bound:
Every real root on lies between and .
and

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