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krok68 [10]
3 years ago
15

Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.

Mathematics
1 answer:
Mariana [72]3 years ago
7 0

Answer:

  f(x) = x^4 +4x^3 +5x^2 +4x +4

Step-by-step explanation:

If "a" is a zero, then (x-a) is a factor. The conjugate of a complex zero is also a zero if the polynomial has real coefficients. Then the factorization is ...

  f(x) = (x -(-2))(x -(-2))(x -i)(x -(-i)) = (x^2 +4x +4)(x^2 +1)

  f(x) = x^4 +4x^3 +5x^2 +4x +4

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