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Find a function of the form ax³ + bx² + cx + d where a, b, c, d are real numbers, and the zeros include 2 and 3-4i.

a) x⁴ + 2x³ + 3x² + 4x - 5
b) x³ + 2x² - 3x - 4
c) x³ - 2x² - 3x + 4
d) x³ - 2x² + 3x - 4

1 Answer

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Final answer:

The function of the given form where the zeros include 2 and 3-4i is represented by the equation x³ - 2x² + 3x - 4 (option d).

Step-by-step explanation:

The function of the form ax³ + bx² + cx + d where a, b, c, and d are real numbers, and the zeros include 2 and 3-4i is represented by the equation x³ - 2x² + 3x - 4 (option d). To determine the function, we can use the zeros and rewrite them as factors of the polynomial. Since the zero is 2, we have a factor (x - 2). Similarly, since the zero is 3-4i, the conjugate 3+4i is also zero, giving us another factor ((x - (3-4i))(x - (3+4i))). By multiplying these factors together, we get the desired function.

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