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

Question

2 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] · Answer 1 · 2022-09-12T13:34:52+03:00

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