4.5x⋅109×8⋅12

Write the polynomial as a function of x.

f(x)=4.5x⋅(109×8)⋅12

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

4.5,109,12

Arrange the terms in ascending order.

b1=|12|,|4.5|,|109|

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

b1=|109|

Simplify each term.

Raise 10 to the power of 9.

b1=|1000000000|+1

The absolute value is the distance between a number and zero. The distance between 0 and 1000000000 is 1000000000.

b1=1000000000+1

b1=1000000000+1

Add 1000000000 and 1.

b1=1000000001

b1=1000000001

Simplify each term.

The absolute value is the distance between a number and zero. The distance between 0 and 4.5 is 4.5.

b2=4.5+|109|+|12|

Raise 10 to the power of 9.

b2=4.5+|1000000000|+|12|

The absolute value is the distance between a number and zero. The distance between 0 and 1000000000 is 1000000000.

b2=4.5+1000000000+|12|

12 is approximately 0.5 which is positive so remove the absolute value

b2=4.5+1000000000+12

b2=4.5+1000000000+12

Find the common denominator.

Write 4.5 as a fraction with denominator 1.

b2=4.51+1000000000+12

Multiply 4.51 by 22.

b2=4.51⋅22+1000000000+12

Multiply 4.51 and 22.

b2=4.5⋅22+1000000000+12

Write 1000000000 as a fraction with denominator 1.

b2=4.5⋅22+10000000001+12

Multiply 10000000001 by 22.

b2=4.5⋅22+10000000001⋅22+12

Multiply 10000000001 and 22.

b2=4.5⋅22+1000000000⋅22+12

b2=4.5⋅22+1000000000⋅22+12

Combine fractions.

Combine fractions with similar denominators.

b2=4.5⋅2+1000000000⋅2+12

Multiply.

Multiply 4.5 by 2.

b2=9+1000000000⋅2+12

Multiply 1000000000 by 2.

b2=9+2000000000+12

b2=9+2000000000+12

b2=9+2000000000+12

Simplify the numerator.

Add 9 and 2000000000.

b2=2000000009+12

Add 2000000009 and 1.

b2=20000000102

b2=20000000102

Divide 2000000010 by 2.

b2=1000000005

Arrange the terms in ascending order.

b2=1,1000000005

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

b2=1000000005

b2=1000000005

Take the smaller bound option between b1=1000000001 and b2=1000000005.

Smaller Bound: 1000000001

Every real root on f(x)=4.5x⋅(109×8)⋅12 lies between -1000000001 and 1000000001.

-1000000001 and 1000000001

Find the Bounds of the Zeros 4.5x*10^9x^8*1/2