# Find the Bounds of the Zeros f(x)=-x^3+3x^2+6x-8

f(x)=-x3+3×2+6x-8
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree: 3
Simplify each term.
Multiply (-x3)⋅-1.
Multiply -1 by -1.
f(x)=1×3+3×2⋅-1+6x⋅-1+(-8)⋅-1
Multiply x3 by 1.
f(x)=x3+3×2⋅-1+6x⋅-1+(-8)⋅-1
f(x)=x3+3×2⋅-1+6x⋅-1+(-8)⋅-1
Multiply -1 by 3.
f(x)=x3-3×2+6x⋅-1+(-8)⋅-1
Multiply -1 by 6.
f(x)=x3-3×2-6x+(-8)⋅-1
Multiply -8 by -1.
f(x)=x3-3×2-6x+8
f(x)=x3-3×2-6x+8
Create a list of the coefficients of the function except the leading coefficient of 1.
-3,-6,8
There will be two bound options, b1 and b2, 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 1.
Arrange the terms in ascending order.
b1=|-3|,|-6|,|8|
The maximum value is the largest value in the arranged data set.
b1=|8|
The absolute value is the distance between a number and zero. The distance between 0 and 8 is 8.
b1=8+1
b1=9
b1=9
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than 1, use that number. If not, use 1.
Simplify each term.
The absolute value is the distance between a number and zero. The distance between -3 and 0 is 3.
b2=3+|-6|+|8|
The absolute value is the distance between a number and zero. The distance between -6 and 0 is 6.
b2=3+6+|8|
The absolute value is the distance between a number and zero. The distance between 0 and 8 is 8.
b2=3+6+8
b2=3+6+8
b2=9+8
b2=17
b2=17
Arrange the terms in ascending order.
b2=1,17
The maximum value is the largest value in the arranged data set.
b2=17
b2=17
Take the smaller bound option between b1=9 and b2=17.
Smaller Bound: 9
Every real root on f(x)=-x3+3×2+6x-8 lies between -9 and 9.
-9 and 9
Find the Bounds of the Zeros f(x)=-x^3+3x^2+6x-8