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The zeros of a rational function g are -3 and 4 Which of the following expressions could define

g?

a. (x−3)(x+4)/(x−2)(x+5)
b. (x−2)(x+5)/(x−3)(x+4)
c.(x−3)(x+5)/(x−3)(x+4)

User Spar
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1 Answer

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Final answer:

None of the provided options correctly define the rational function with zeros at -3 and 4. Option a) has zeros at 3 and -4, b) has poles at -3 and 4, and c) can be simplified to have a single zero, which is not at -3. If an expression with the matching zeros existed, it would probably be similar to option a) but with different signs.

Step-by-step explanation:

To determine which expression could define the rational function g with zeros at -3 and 4, we analyze the given options. A function's zeros are the x-values for which the numerator of the function is equal to zero. For option a) (x−3)(x+4)/(x−2)(x+5), the zeros of the function would be x = 3 and x = -4 which does not match our required zeros. For option b) (x−2)(x+5)/(x−3)(x+4), the values -3 and 4 would actually make the denominator equal to zero, which are not zeros, but rather poles of the rational function. Lastly, option c) (x−3)(x+5)/(x−3)(x+4) can be simplified to (x+5)/(x+4) because the (x−3) terms cancel out. This leaves us without a zero at -3. None of the given options yield the exact zeros of -3 and 4, but if we had to choose the expression that could be modified to those specific zeros, we would possibly modify option a) by adjusting the signs: (x+3)(x-4)/(x−2)(x+5). However, this is not listed among the choices provided.

User Ricardo Faria
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