f(x)=x3-16×2+63x

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.

Largest Degree: 3

Leading Coefficient: 1

Create a list of the coefficients of the function except the leading coefficient of 1.

-16,63

Arrange the terms in ascending order.

b1=|-16|,|63|

The maximum value is the largest value in the arranged data set.

b1=|63|

The absolute value is the distance between a number and zero. The distance between 0 and 63 is 63.

b1=63+1

Add 63 and 1.

b1=64

b1=64

Simplify each term.

The absolute value is the distance between a number and zero. The distance between -16 and 0 is 16.

b2=16+|63|

The absolute value is the distance between a number and zero. The distance between 0 and 63 is 63.

b2=16+63

b2=16+63

Add 16 and 63.

b2=79

Arrange the terms in ascending order.

b2=1,79

The maximum value is the largest value in the arranged data set.

b2=79

b2=79

Take the smaller bound option between b1=64 and b2=79.

Smaller Bound: 64

Every real root on f(x)=x3-16×2+63x lies between -64 and 64.

-64 and 64

Find the Bounds of the Zeros f(x)=x^3-16x^2+63x