p(x)=x2-5x+2

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

Largest Degree: 2

Leading Coefficient: 1

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

-5,2

Arrange the terms in ascending order.

b1=|2|,|-5|

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

b1=|-5|

The absolute value is the distance between a number and zero. The distance between -5 and 0 is 5.

b1=5+1

Add 5 and 1.

b1=6

b1=6

Simplify each term.

The absolute value is the distance between a number and zero. The distance between -5 and 0 is 5.

b2=5+|2|

The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.

b2=5+2

b2=5+2

Add 5 and 2.

b2=7

Arrange the terms in ascending order.

b2=1,7

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

b2=7

b2=7

Take the smaller bound option between b1=6 and b2=7.

Smaller Bound: 6

Every real root on p(x)=x2-5x+2 lies between -6 and 6.

-6 and 6

Find the Bounds of the Zeros p(x)=x^2-5x+2