# Find the Bounds of the Zeros f(x)=-2x^4+25x^3-95x^2+90x+72

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Dividing two negative values results in a positive value.
Cancel the common factor of and .
Factor out of .
Move the negative one from the denominator of .
Rewrite as .
Multiply by .
Divide by .
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.
is approximately which is positive so remove the absolute value
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
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.
is approximately which is negative so negate and remove the absolute value
is approximately which is positive so remove the absolute value
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 .
Combine fractions.
Combine fractions with similar denominators.
Simplify the expression.
Divide by .