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
