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:
Leading Coefficient:
Simplify each term.
Tap for more steps...
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor.
Divide by to get .
Divide 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 .
Tap for more steps...
Arrange the terms in ascending order.
The absolute value is the distance between a number and zero. The distance between and is .
Add and to get .
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 .
Tap for more steps...
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.
Take the smaller bound option between and .
Smaller Bound:
Every real root on lies between and .
and
Enter YOUR Problem
Mathway requires javascript and a modern browser.