Chapter 4: Q. 25 (page 215)

use the given zero to find the remaining zeros of each function.
$f (x) = 2 x^{4} + 5 x^{3} + 5 x^{2} + 20 x - 12; z e r o : - 2 i$

Short Answer

Expert verified

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

Step by step solution

Given information

We are given a polynomial $f (x) = 2 x^{4} + 5 x^{3} + 5 x^{2} + 20 x - 12$

Find the zeros by synthetic divsion

We have,

$f (x) = 2 x^{4} + 5 x^{3} + 5 x^{2} + 20 x - 12$ and 2i as one of the root

$2 i 2 5 5 20 - 12 4 i 10 i - 8 - 20 - 6 i 12 2 5 + 4 i 10 i - 3 - 6 i 0$

as 2i is one root then -2i is the second root

$- 2 i 2 5 + 4 i 10 i - 3 - 6 i - 4 i - 10 i 6 i 2 5 - 3 0$

Now we have,

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

Now we factor the remaining term

$2 x^{2} + 5 x - 3 = 0 (2 x - 1) (x + 3) = 0 ∴ x = \frac{1}{2} o r x = - 3$

Conclusion

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

use the given zero to find the remaining zeros of each function.
$f (x) = 2 x^{4} + 5 x^{3} + 5 x^{2} + 20 x - 12; z e r o : - 2 i$

Short Answer

Step by step solution

Given information

Find the zeros by synthetic divsion

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

use the given zero to find the remaining zeros of each function. f(x)=2x4+5x3+5x2+20x-12;zero:-2i

Short Answer

Step by step solution

Given information

Find the zeros by synthetic divsion

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

use the given zero to find the remaining zeros of each function.
$f (x) = 2 x^{4} + 5 x^{3} + 5 x^{2} + 20 x - 12; z e r o : - 2 i$