Chapter 4: Q. 31 (page 215)

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{3} - 1$

Short Answer

Expert verified

The complex root of the polynomial are $\frac{- 1 + 3 i}{2}, \frac{- 1 - 3 i}{2}$ .

Step by step solution

Given information

We are given a polynomial $f (x) = x^{3} - 1$

Find the zeros of the polynomial

We get,

$x^{3} - 1 = 0 (x - 1) (x^{2} + x + 1) = 0$

Now we use quadratic formula to find the remaining factors

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- 1 \pm \sqrt{1 - 4}}{2} x = \frac{- 1 \pm \sqrt{- 3}}{2} x = \frac{- 1 \pm 3 i}{2}$

Conclusion

The complex roots of the polynomial are $\frac{- 1 + 3 i}{2}, \frac{- 1 - 3 i}{2}$

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find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{3} - 1$

Short Answer

Step by step solution

Given information

Find the zeros of the polynomial

Conclusion

One App. One Place for Learning.

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find the complex zeros of each polynomial function. Write f in factored form.f(x)=x3-1

Short Answer

Step by step solution

Given information

Find the zeros of the polynomial

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{3} - 1$