Chapter 4: Q. 45 (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.
$Z e r o s : - 4, - 1, 2, 3; d e g r e e 4$

Short Answer

Expert verified

The polynomial function is $f (x) = x^{4} - 15 x^{2} + 10 x + 24$ with degree 4.

Step by step solution

Step 1. Given Information

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

Step 2. Forming the polynomial Function

If $r$ a real zero of a polynomial function of $f,$ then $x - r$ is a factor of $f .$ This means that $x - (- 4) = x + 4$ and $(x + 1), (x - 2), (x - 3)$ are the factors of $f .$ Any polynomial function is of the form $f (x) = a (x + 4) (x + 1) (x - 2) (x - 3) i f a = 1 f (x) = (x + 4) (x + 1) (x - 2) (x - 3)$

Step 3. Solving Polynomial Function

$f (x) = (x + 4) (x + 1) (x - 2) (x - 3) f (x) = (x^{2} + 5 x + 4) (x^{2} - 5 x + 6) f (x) = (x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{3} - 25 x^{2} + 30 x + 4 x^{2} - 20 x + 24) f (x) = x^{4} - 15 x^{2} + 10 x + 24$

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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.
$Z e r o s : - 4, - 1, 2, 3; d e g r e e 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming the 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:-4,-1,2,3;degree4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming the polynomial Function

Step 3. Solving Polynomial Function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Calculus

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.
$Z e r o s : - 4, - 1, 2, 3; d e g r e e 4$