# Find the Bounds of the Zeros f(x)=-15x^3+30x^2+17x-45

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 .
Cancel the common factor of and .
Factor out of .
Move the negative one from the denominator of .
Rewrite as .
Multiply by .
Move the negative in front of the fraction.
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.
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 .
is approximately which is negative so negate and remove the absolute value
The absolute value is the distance between a number and zero. The distance between and is .
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine fractions.
Combine fractions with similar denominators.
Multiply.
Multiply by .
Multiply by .
Simplify the numerator.
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
Find the Bounds of the Zeros f(x)=-15x^3+30x^2+17x-45