111k views
22 votes
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree 6; zeros: -1, 2 + i, -3 - i, 0

1 Answer

8 votes

Answer:

The remaining zeros of f is (2 - i) and (-3 + i).

Explanation:

We are given a degree six polynomial f and four of its zeros:


\displaystyle x = -1, 2+i, -3-i, 0

And we want to find the remaining zeros of f.

By the Fundamental Theorem of Algebra, the number of zeros of any polynomial is equal to its degree.

Hence, a sixth degree polynomial must have six zeros.

Because we are given four zeros, f has two more zeros.

To find the remaining two zeros, recall the Complex Conjugate Root Theorem:

\displaystyle \text{If } a+bi \text{ is a zero, then } a-bi\text{ is also a zero.}

Our two complex zeros are (2 + i) and (-3 - i).

Then by the above theorem, (2 - i) and (-3 + i) is the two remaining zeros of f.

User Promit
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories