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A quadratic function has zeros at -4/3 and 2/3. One factor of this function must be

a. 2x - 3
b. 3x - 4
с. 4x - 3
d. 3x - 2

1 Answer

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Final answer:

The factor of the quadratic function corresponding to the zero at 2/3 is 3x - 2; therefore, the correct answer is d. 3x - 2.

Step-by-step explanation:

The student has asked for help with determining one factor of a quadratic function that has zeros at -4/3 and 2/3. A zero of a quadratic function corresponds to the x-value where the function equals zero, and can be represented by the factor (x - zero). Therefore, if the function has a zero at -4/3, one factor must be (x - (-4/3)) or (x + 4/3), and if the other zero is at 2/3, the factor must be (x - 2/3).

When we clear the fractions in these expressions, we multiply the inside of the parentheses by 3 to get rid of the denominator, resulting in factors of 3x + 4 and 3x - 2. The correct factor that corresponds to one of these zeros and is available in the options provided by the student is 3x - 2, which corresponds to the zero at 2/3.

The answer to the question is d. 3x - 2.

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