f(x)=x3+6×2-36x+50

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.

6,-36,50

Arrange the terms in ascending order.

b1=|6|,|-36|,|50|

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

b1=|50|

The absolute value is the distance between a number and zero. The distance between 0 and 50 is 50.

b1=50+1

Add 50 and 1.

b1=51

b1=51

Simplify each term.

The absolute value is the distance between a number and zero. The distance between 0 and 6 is 6.

b2=6+|-36|+|50|

The absolute value is the distance between a number and zero. The distance between -36 and 0 is 36.

b2=6+36+|50|

The absolute value is the distance between a number and zero. The distance between 0 and 50 is 50.

b2=6+36+50

b2=6+36+50

Simplify by adding numbers.

Add 6 and 36.

b2=42+50

Add 42 and 50.

b2=92

b2=92

Arrange the terms in ascending order.

b2=1,92

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

b2=92

b2=92

Take the smaller bound option between b1=51 and b2=92.

Smaller Bound: 51

Every real root on f(x)=x3+6×2-36x+50 lies between -51 and 51.

-51 and 51

Find the Bounds of the Zeros f(x)=x^3+6x^2-36x+50