Pre-Algebra Examples

Find the Bounds of the Zeros f(x)=-16x^2+42(9)+12
Step 1
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Leading Coefficient:
Step 2
The leading coefficient needs to be . If it is not, divide the expression by it to make it .
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Multiply by .
Step 2.3
Add and .
Step 2.4
Cancel the common factor of and .
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Step 2.4.1
Factor out of .
Step 2.4.2
Factor out of .
Step 2.4.3
Factor out of .
Step 2.4.4
Cancel the common factors.
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Step 2.4.4.1
Factor out of .
Step 2.4.4.2
Cancel the common factor.
Step 2.4.4.3
Rewrite the expression.
Step 2.5
Move the negative in front of the fraction.
Step 2.6
Factor out of .
Step 2.7
Rewrite as .
Step 2.8
Factor out of .
Step 2.9
Rewrite as .
Step 2.10
Move the negative in front of the fraction.
Step 2.11
Multiply by .
Step 2.12
Multiply by .
Step 3
Create a list of the coefficients of the function except the leading coefficient of .
Step 4
There will be two bound options, and , 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 .
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Step 4.1
Arrange the terms in ascending order.
Step 4.2
Add and .
Step 5
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than , use that number. If not, use .
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Step 5.1
Arrange the terms in ascending order.
Step 5.2
The maximum value is the largest value in the arranged data set.
Step 6
The bound options are the same.
Bound:
Step 7
Every real root on lies between and .
and