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f(x)= 3x^3 -23x^2 -29x -7 List all possible (or potential) rational zeros for the...
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High School Teacher
Potential rational zeros for a polynomial are found by taking combinations of the factors of the last term and dividing by the factors of the first term. In the function f(x), the factors of 7 are 1 and 7. The factors of 3 are 1 and 3. A list of possible rational zeros are:
`+-1, +-7, +-1/3, +-7/3`
Using the list of possible rational zeros, the graph shows that -1/3 has good possibilities of being a rational zero.
Checking -1/3 using synthetic division does yield a zero remainder.
Therefore, -1/3 is a real rational zero. To find the remaining zeros, divide f(x) by the factor (3x+1).
Find the remaining zeros using the quadratic formula:
The three roots are: -1/3 , 4+sqrt(23), and 4-sqrt(23)
The factors are : `(3x+1)(x-4-sqrt(23))(x-4+sqrt(23))`
Posted by taylormath on February 14, 2012 at 10:57 AM (Answer #1)
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