Chapter 4: Q. 8 (page 247)

Write a function that meets the given conditions.
Fourth-degree polynomial function with real coefficients; zeros: $- 2, 0, 3 + i$

Short Answer

Expert verified

The polynomial function is $f (x) = x^{4} - 4 x^{3} - 2 x^{2} + 20 x$

Step by step solution

Step 1. Given Information

The given conditions are fourth-degree polynomial function with real coefficients; zeros: $- 2, 0, 3 + i$

Explanation

Since, the polynomial has a degree 4, the polynomial will have 4 zeroes.

Thus, $3 - i$ must also be a zero of the function.

Use the factor theorem and distributive property to find the polynomial.

localid="1646309910774" $f (x) = a (x + 2) (x + 0) [x - (3 + i)] [x - (3 - i)] = a x (x + 2) [x^{2} - 3 x + x i - 3 x - x i + 9 - i^{2}] = a (x^{2} + 2 x) [x^{2} - 6 x + 10] = a (x^{4} - 6 x^{3} + 10 x^{2} + 2 x^{3} - 12 x^{2} + 20 x) = a (x^{4} - 4 x^{3} - 2 x^{2} + 20 x)$

Let $a = 1$ then the required polynomial is $x^{4} - 4 x^{3} - 2 x^{2} + 20 x$

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Write a function that meets the given conditions.
Fourth-degree polynomial function with real coefficients; zeros: $- 2, 0, 3 + i$

Short Answer

Step by step solution

Step 1. Given Information

Explanation

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Write a function that meets the given conditions.Fourth-degree polynomial function with real coefficients; zeros:-2,0,3+i

Short Answer

Step by step solution

Step 1. Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Mechanics Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Write a function that meets the given conditions.
Fourth-degree polynomial function with real coefficients; zeros: $- 2, 0, 3 + i$