p(x)=x3-9×2+25x-17

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.

-9,25,-17

Arrange the terms in ascending order.

b1=|-9|,|-17|,|25|

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

b1=|25|

The absolute value is the distance between a number and zero. The distance between 0 and 25 is 25.

b1=25+1

Add 25 and 1.

b1=26

b1=26

Simplify each term.

The absolute value is the distance between a number and zero. The distance between -9 and 0 is 9.

b2=9+|25|+|-17|

The absolute value is the distance between a number and zero. The distance between 0 and 25 is 25.

b2=9+25+|-17|

The absolute value is the distance between a number and zero. The distance between -17 and 0 is 17.

b2=9+25+17

b2=9+25+17

Simplify by adding numbers.

Add 9 and 25.

b2=34+17

Add 34 and 17.

b2=51

b2=51

Arrange the terms in ascending order.

b2=1,51

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

b2=51

b2=51

Take the smaller bound option between b1=26 and b2=51.

Smaller Bound: 26

Every real root on p(x)=x3-9×2+25x-17 lies between -26 and 26.

-26 and 26

Find the Bounds of the Zeros p(x)=x^3-9x^2+25x-17