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Chapter 4: Q. 36 (page 215)

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{4} + 13 x^{2} + 36$

Short Answer

Expert verified

The roots of the given polynomial $3 i, - 3 i, 2 i, - 2 i$

Step by step solution

01

Given information

We are given a polynomial $f (x) = x^{4} + 13 x^{2} + 36$

02

Factor the given polynomial

We get,

$x^{4} + 13 x^{2} + 36 = 0 (x^{2} + 9) (x^{2} + 4) = 0 (x - 3 i) (x + 3 i) (x - 2 i) (x + 2 i) = 0$

03

Conclusion

The roots of the given polynomial is $3 i, - 3 i, 2 i, - 2 i$

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Most popular questions from this chapter

Find a rational function that might have the given graph.

Find the real zeros of f. Use the real zeros to factor f.

$f (x) = x^{3} + 6 x^{2} + 6 x - 4$

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = x^{5} - x^{4} + 2 x^{2} + 3$

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.

Solve the inequality algebraically

$(x + 1) (x + 2) (x + 3) \leq 0$

See all solutions

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