Chapter 4: Q. 46 (page 194)

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 3, - 1, 2, 5; d e g r e e 4$

Short Answer

Expert verified

The polynomial function is $f (x) = x^{4} - 3 x^{3} - 15 x^{2} + 19 x + 30$ with degree 4.

Step by step solution

Step 1. Given Information

The zeros of the polynomial are $- 3, - 1, 2, 5$ and degree is 4

Step 2. Forming Polynomial Function

If $r$ is a real zero of a polynomial function $f,$ then $x - r$ is a factor of $f .$ This means that $x - (- 3) = (x + 3) a n d (x + 1), (x - 2), (x - 5)$ . As a result, any polynomial function is of the form $f (x) = (x + 3) (x + 1) (x - 2) (x - 5)$

Step 3. Solving polynomial function

$f (x) = (x + 3) (x + 1) (x - 2) (x - 5) f (x) = (x^{2} + 4 x + 3) (x^{2} - 7 x + 10) f (x) = (x^{4} - 7 x^{3} + 10 x^{2} + 4 x^{3} - 28 x^{2} + 40 x + 3 x^{2} - 21 x + 30) f (x) = x^{4} - 3 x^{3} - 15 x^{2} + 19 x + 30$

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In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 3, - 1, 2, 5; d e g r e e 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming Polynomial Function

Step 3. Solving polynomial function

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In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.Zeros:-3,-1,2,5;degree4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming Polynomial Function

Step 3. Solving polynomial function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 3, - 1, 2, 5; d e g r e e 4$