Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.
1 answer:
Answer:
Step-by-step explanation:
If the polynomial has one root as 1 + i, it's conjugate 1 - i will also be its root.
Therefore, the polynomial has roots 1 + i, 1 - i, and 3.
So, the polynomial function of lowest degree with rational coefficients will be
f (x) = (x - 3)(x - 1 - i)(x - 1 + i)
⇒
⇒
⇒ (Answer)
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Option D: are the ordered pairs represents a function.
Explanation:
Given that the options of the set of ordered pairs.
We need to determine the ordered pairs that represents a function.
Option A:
A relation is said to be a function if each element of x is related to exactly one element in y.
From this set of ordered pairs, it is obvious that the element -12 of x is related to two different element in y.
Thus, the ordered pairs is not a function.
Hence, Option A is not the correct answer.
Option B:
From this set of ordered pairs, it is obvious that the elements -8 and 8 of x are related to two different element in y.
Thus, the ordered pairs is not a function.
Hence, Option B is not the correct answer.
Option C:
From this set of ordered pairs, it is obvious that the element 13 of x is related to three different element in y.
Thus, the ordered pairs is not a function.
Hence, Option C is not the correct answer.
Option D:
A relation is said to be a function if each element of x is related to exactly one element in y.
From this set of ordered pairs, it is obvious that the each element of x is related exactly one element in y.
Thus, the ordered pairs is a function.
Hence, Option D is the correct answer.