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lesya [120]
3 years ago
13

Write a polynomial f(x) that satisfies the given conditions, Express the polynomial with the lowest possible leading positive in

teger coefficient
Polynomial of lowest degree with lowest possible integer coefficients, and with zeros 5-8i and 0 (multiplicity 4).
Mathematics
1 answer:
RUDIKE [14]3 years ago
4 0

9514 1404 393

Answer:

  f(x) = x^6 -10x^5 +89x^4

Step-by-step explanation:

For a given zero p with multiplicity n, one of the factors of the polynomial will be (x -p)^n. If the polynomial has real coefficients, then the complex zeros come in conjugate pairs.

The factored form of your polynomial is ...

  f(x) = (x -(5 -8i))(x -(5 +8i))(x -0)^4

  f(x) = ((x -5)^2 -(8i)^2)(x^4) = (x^2 -10x +89)(x^4)

  f(x) = x^6 -10x^5 +89x^4

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Answer:

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D) The las runner finishes the race at point D.

Then the first runner that finishes the race is the one with the shorter graph (shorter graph means that he ran for less time than the others, wich means that he/she finished first)

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