Chapter 4: Q. 37 (page 215)

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75$

Short Answer

Expert verified

The complex roots of the polynomial is $5 i, - 5 i$

Step by step solution

Given information

We are given a polynomial $f (x) = x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75$

Factor the polynomial

We get,

$x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75 = 0 x^{4} + 2 x^{3} - 3 x^{2} + 25 x^{2} + 50 x - 75 = 0 x^{2} (x^{2} + 2 x - 3) + 25 (x^{2} + 2 x - 3) = 0 (x^{2} + 25) (x^{2} + 2 x - 3) = 0 (x - 5 i) (x + 5 i) (x + 3) (x - 1) = 0$

Conclusion

The complex roots of the polynomial are $5 i, - 5 i$

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find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75$

Short Answer

Step by step solution

Given information

Factor the polynomial

Conclusion

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find the complex zeros of each polynomial function. Write f in factored form. f(x)=x4+2x3+22x2+50x-75

Short Answer

Step by step solution

Given information

Factor the polynomial

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

find the complex zeros of each polynomial function. Write f in factored form.
$f (x) = x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75$