Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

Giltrapsx

Giltrapsx

Open question

2022-08-20

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

Answer & Explanation

Randy Kaiser

Randy Kaiser

Beginner2022-08-21Added 5 answers

Q has degree 3, and zeros 0 and i.
Since i is a zero, then so is -i by the Conjugate Zeros
Theorem. This means that has the form
Q(x)=a(x-0)(x+i)(x-i)
Expand and simplify
Q(x)=a(x3+x)
Let a=1
Q(x)=x3+x
Any other polynomial that satisfies the given requirements must be an integer multiple of this one.
Result:
Q(x)=x3+x

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?