Chapter 4: Q. 22 (page 215)

form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.
Degree 4; zeros: 1 multiplicity 3 ; 1+i

Short Answer

Expert verified

The polynomial can be given as $f (x) = x^{5} - 5 x^{4} + 11 x^{3} + 13 x^{2} + 8 x - 2$

Step by step solution

Given information

We are given the degree of polynomial to be 5 the zeros are 1+i and 1 with multiplicity 3

Find the equation

As 1+i is one of the roots of the polynomial by conjugate property 1-i is also a root of the polynomial

Hence,

$f (x) = (x - 1) (x - 1) (x - 1) (x - (1 + i)) (x - (1 - i)) f (x) = {(x - 1)}^{3} ({(x - 1)}^{2} + 1) f (x) = (x^{3} - 3 x^{2} + 3 x - 1) (x^{2} - 2 x + 2) f (x) = x^{5} - 5 x^{4} + 11 x^{3} + 13 x^{2} + 8 x - 2$

Conclusion

The polynomial can be given as $f (x) = x^{5} - 5 x^{4} + 11 x^{3} + 13 x^{2} + 8 x - 2$

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form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.
Degree 4; zeros: 1 multiplicity 3 ; 1+i

Short Answer

Step by step solution

Given information

Find the equation

Conclusion

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form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.Degree 4; zeros: 1 multiplicity 3 ; 1+i

Short Answer

Step by step solution

Given information

Find the equation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Geometry

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.
Degree 4; zeros: 1 multiplicity 3 ; 1+i