# Find the Bounds of the Zeros 3x(x+7) 3x(x+7)
Write the polynomial as a function of x.
f(x)=3x(x+7)
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree: 2
The leading coefficient needs to be 1. If it is not, divide the expression by it to make it 1.
Cancel the common factor of 3.
Cancel the common factor.
f(x)=3x(x+7)3
Divide x(x+7) by 1.
f(x)=x(x+7)
f(x)=x(x+7)
Apply the distributive property.
f(x)=x⋅x+x⋅7
Simplify the expression.
Multiply x by x.
f(x)=x2+x⋅7
Move 7 to the left of x.
f(x)=x2+7x
f(x)=x2+7x
f(x)=x2+7x
Create a list of the coefficients of the function except the leading coefficient of 1.
7
There will be two bound options, b1 and b2, the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add 1.
Arrange the terms in ascending order.
b1=|7|
The absolute value is the distance between a number and zero. The distance between 0 and 7 is 7.
b1=7+1
Add 7 and 1.
b1=8
b1=8
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than 1, use that number. If not, use 1.
The absolute value is the distance between a number and zero. The distance between 0 and 7 is 7.
b2=7
Arrange the terms in ascending order.
b2=1,7
The maximum value is the largest value in the arranged data set.
b2=7
b2=7
Take the smaller bound option between b1=8 and b2=7.
Smaller Bound: 7
Every real root on f(x)=3x(x+7) lies between -7 and 7.
-7 and 7
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