How to find a polynomial function of lowest degree with rational coefficients that has the given number of some of it's zeros. -5i, 3?

kwokmichellevc9

kwokmichellevc9

Answered question

2023-03-14

How to find a polynomial function of lowest degree with rational coefficients that has the given number of some of it's zeros. -5i, 3?

Answer & Explanation

advibrimbmw1

advibrimbmw1

Beginner2023-03-15Added 4 answers

Any complex zeros will appear in conjugate pairs if the coefficients are real, much alone rational.
So the roots of f ( x ) = 0 are at least ± 5 i and 3
Thus
f ( x ) = ( x - 5 i ) ( x + 5 i ) ( x - 3 )
= ( x 2 + 25 ) ( x - 3 ) = x 3 - 3 x 2 + 25 x - 75
These zeros guarantee that any polynomial in x is a multiple of f. (x)

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