Chapter 4: Q. 34 (page 215)

find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} + 13 x^{2} + 57 x + 85$

Short Answer

Expert verified

The complex roots of the polynomial are 4+i and 4-i

Step by step solution

Given information

We are given a polynomial $f (x) = x^{3} + 13 x^{2} + 57 x + 85$

Find the factors

To find the factors of the polynomial we first have to find the factors of 85,

They can be given as $\pm 1, \pm 5, \pm 17, \pm 85$

Let us try -5 using synthetic division

role="math" localid="1647572985088" $- 5 1 13 57 85 - 5 - 40 - 85 1 8 17 0$

hence the polynomial becomes

role="math" localid="1647573001820" $f (x) = (x + 5) (x^{2} + 8 x + 17) N o w w e u s e q u a d r a t i c f o r m u l a t o f i n d t h e r e m a i n i n g f a c t o r s x = \frac{- 8 \pm \sqrt{64 - 68}}{2} x = \frac{- 8 \pm 2 i}{2} x = 4 \pm i$

Conclusion

The complex roots of the polynomial are 4+i and 4-i

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find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} + 13 x^{2} + 57 x + 85$

Short Answer

Step by step solution

Given information

Find the factors

Conclusion

One App. One Place for Learning.

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find the complex zeros of each polynomial function. Write f in factored formf(x)=x3+13x2+57x+85

Short Answer

Step by step solution

Given information

Find the factors

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} + 13 x^{2} + 57 x + 85$