p(x)=-1.2×2+62.5x-491

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

Largest Degree: 2

Leading Coefficient: -1.2

Cancel the common factor of -1.2.

Cancel the common factor.

p(x)=-1.2×2-1.2+62.5x-1.2+-491-1.2

Divide x2 by 1.

p(x)=x2+62.5x-1.2+-491-1.2

p(x)=x2+62.5x-1.2+-491-1.2

Move the negative in front of the fraction.

p(x)=x2-62.5×1.2+-491-1.2

Factor 62.5 out of 62.5x.

p(x)=x2-62.5(x)1.2+-491-1.2

Factor 1.2 out of 1.2.

p(x)=x2-62.5(x)1.2(1)+-491-1.2

Separate fractions.

p(x)=x2-(62.51.2⋅x1)+-491-1.2

Divide 62.5 by 1.2.

p(x)=x2-(52.083‾(x1))+-491-1.2

Divide x by 1.

p(x)=x2-(52.083‾x)+-491-1.2

Multiply 52.083‾ by -1.

p(x)=x2-52.083‾x+-491-1.2

Divide -491 by -1.2.

p(x)=x2-52.083‾x+409.16‾

p(x)=x2-52.083‾x+409.16‾

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

-52.083‾,409.16‾

Arrange the terms in ascending order.

b1=|-52.083‾|,|409.16‾|

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

b1=|409.16‾|

The absolute value is the distance between a number and zero. The distance between 0 and 409.16‾ is 409.16‾.

b1=409.16‾+1

Add 409.16‾ and 1.

b1=410.16‾

b1=410.16‾

Simplify each term.

The absolute value is the distance between a number and zero. The distance between -52.083‾ and 0 is 52.083‾.

b2=52.083‾+|409.16‾|

The absolute value is the distance between a number and zero. The distance between 0 and 409.16‾ is 409.16‾.

b2=52.083‾+409.16‾

b2=52.083‾+409.16‾

Add 52.083‾ and 409.16‾.

b2=461.25

Arrange the terms in ascending order.

b2=1,461.25

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

b2=461.25

b2=461.25

Take the smaller bound option between b1=410.16‾ and b2=461.25.

Smaller Bound: 410.16‾

Every real root on p(x)=-1.2×2+62.5x-491 lies between -410.16‾ and 410.16‾.

-410.16‾ and 410.16‾

Find the Bounds of the Zeros p(x)=-1.2x^2+62.5x-491