p(x)=2.75×4-3×2+5x+2

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

Largest Degree: 4

Leading Coefficient: 2.75

Cancel the common factor of 2.75.

Cancel the common factor.

p(x)=2.75×42.75+-3×22.75+5×2.75+22.75

Divide x4 by 1.

p(x)=x4+-3×22.75+5×2.75+22.75

p(x)=x4+-3×22.75+5×2.75+22.75

Move the negative in front of the fraction.

p(x)=x4-(3)x22.75+5×2.75+22.75

Factor 3 out of 3×2.

p(x)=x4-3(x2)2.75+5×2.75+22.75

Factor 2.75 out of 2.75.

p(x)=x4-3(x2)2.75(1)+5×2.75+22.75

Separate fractions.

p(x)=x4-(32.75⋅x21)+5×2.75+22.75

Divide 3 by 2.75.

p(x)=x4-(1.09‾(x21))+5×2.75+22.75

Divide x2 by 1.

p(x)=x4-(1.09‾x2)+5×2.75+22.75

Multiply 1.09‾ by -1.

p(x)=x4-1.09‾x2+5×2.75+22.75

Factor 5 out of 5x.

p(x)=x4-1.09‾x2+5(x)2.75+22.75

Factor 2.75 out of 2.75.

p(x)=x4-1.09‾x2+5(x)2.75(1)+22.75

Separate fractions.

p(x)=x4-1.09‾x2+52.75⋅x1+22.75

Divide 5 by 2.75.

p(x)=x4-1.09‾x2+1.81‾(x1)+22.75

Divide x by 1.

p(x)=x4-1.09‾x2+1.81‾x+22.75

Divide 2 by 2.75.

p(x)=x4-1.09‾x2+1.81‾x+0.72‾

p(x)=x4-1.09‾x2+1.81‾x+0.72‾

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

-1.09‾,1.81‾,0.72‾

Arrange the terms in ascending order.

b1=|0.72‾|,|-1.09‾|,|1.81‾|

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

b1=|1.81‾|

The absolute value is the distance between a number and zero. The distance between 0 and 1.81‾ is 1.81‾.

b1=1.81‾+1

Add 1.81‾ and 1.

b1=2.81‾

b1=2.81‾

Simplify each term.

The absolute value is the distance between a number and zero. The distance between -1.09‾ and 0 is 1.09‾.

b2=1.09‾+|1.81‾|+|0.72‾|

The absolute value is the distance between a number and zero. The distance between 0 and 1.81‾ is 1.81‾.

b2=1.09‾+1.81‾+|0.72‾|

The absolute value is the distance between a number and zero. The distance between 0 and 0.72‾ is 0.72‾.

b2=1.09‾+1.81‾+0.72‾

b2=1.09‾+1.81‾+0.72‾

Simplify by adding numbers.

Add 1.09‾ and 1.81‾.

b2=2.90‾+0.72‾

Add 2.90‾ and 0.72‾.

b2=3.63‾

b2=3.63‾

Arrange the terms in ascending order.

b2=1,3.63‾

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

b2=3.63‾

b2=3.63‾

Take the smaller bound option between b1=2.81‾ and b2=3.63‾.

Smaller Bound: 2.81‾

Every real root on p(x)=2.75×4-3×2+5x+2 lies between -2.81‾ and 2.81‾.

-2.81‾ and 2.81‾

Find the Bounds of the Zeros p(x)=2.75x^4-3x^2+5x+2