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Chapter 4: Q. 35 (page 215)

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{4} + 5 x^{2} + 4$

Short Answer

Expert verified

The zeros of the polynomial are $2 i, - 2 i, i, - i$

Step by step solution

01

Given information

We are given a polynomial $f (x) = x^{4} + 5 x^{2} + 4$

02

Find the zeros

We get,

$x^{4} + 5 x^{2} + 4 = 0 (x^{2} + 4) (x^{2} + 1) = 0 (x - 2 i) (x + 2 i) (x - i) (x + i) = 0$

03

Conclusion

The zeros of the polynomial is $2 i, - 2 i, i, - i$

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Most popular questions from this chapter

Use the Factor Theorem to prove that $x - c$ is a factor of

$x^{n} - c^{n}$ for any positive integer n.

Graph each rational function using transformations.

$R (x) = 1 + \frac{2}{{(x - 3)}^{2}}$

Analyze each polynomial function using Steps $1$ through $8$ :

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

A can in the shape of a right circular cylinder is required to have a volume of $500$ cubic centimeters. The top and bottom are made of material that costs $0.06 ₡$ per square centimeter, while the sides are made of material that costs $0.04 ₡$ per square centimeter.

Part (a) Express the total cost C of the material as a function of the radius r of the cylinder.

Part (b): Graph $C = C (r)$ . For what value of r is the cost C a minimum?

In Problems 63–72, find the real solutions of each equation.

$x^{4} - 2 x^{3} + 10 x^{2} - 18 x + 9 = 0$

See all solutions

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