Chapter 4: Q. 9 (page 215)

Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 4 and zeros are role="math" localid="1646221442495" $i, 1 + i$

Short Answer

Expert verified

The two remaining zeros of the polynomial are $- i, 1 - i$ .

Step by step solution

Step 1. Given Information

The polynomial has degree 4 and two zeros are $i$ and $1 + i$ .

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree $n$ with real coefficient, has one complex zero of the form $a + i b$ then the polynomial should have the conjugate pair of $a + i b$ that is $a - i b$ as another zero.

Step 3. Explanation

Since $f (x)$ has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $- i$ , the conjugate of $i$ , and $1 - i$ , the conjugate of $1 + i$ , are the two remaining zeros.

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Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 4 and zeros are role="math" localid="1646221442495" $i, 1 + i$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

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Find the remaining zeros of fxwith real coefficients and given information.The degree is 4 and zeros are role="math" localid="1646221442495" i,1+i

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

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Study anywhere. Anytime. Across all devices.

Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 4 and zeros are role="math" localid="1646221442495" $i, 1 + i$