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
