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kompoz [17]
3 years ago
6

Write a polynomial function of least degree with integral coefficients that has the given zeros

Mathematics
1 answer:
Zigmanuir [339]3 years ago
6 0

Answer:

x^{4} + 3x² - 4

Step-by-step explanation:

Note that complex zeros occur in conjugate pairs

If 2i is a zero then - 2i is a zero

The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are

(x - 1), (x + 1), (x - 2i) and (x + 2i)

The polynomial is expressed as the product of the factors, thus

f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs

     = (x² - 1)(x² - 4i²) → i² = - 1

     = (x² - 1)(x² + 4) ← distribute

     = x^{4} + 4x² - x² - 4

     = x^{4} + 3x² - 4

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