Chapter 4: Q. 33 (page 215)

find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} - 8 x^{2} + 25 x - 26$

Short Answer

Expert verified

The complex roots of the polynomial are 3+2i, 3-2i

Step by step solution

Given information

We are given a polynomial $f (x) = x^{3} - 8 x^{2} + 25 x - 26$

Find the factors

To find the factors of the polynomial we first find the factors of -26

They can be given as $\pm 1, \pm 2, \pm 13, \pm 26$

Let us test 2 using synthetic division whether we get zero or not

$2 1 - 8 25 - 26 2 - 12 26 1 - 6 13 0$

Hence the polynomial can be given as

$f (x) = (x - 2) (x^{2} - 6 x + 13)$

Now using quadratic formula find the remaining factors

$x^{2} - 6 x + 13 = 0 x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{6 \pm \sqrt{36 - 52}}{2} x = \frac{6 \pm 4 i}{2} x = 3 \pm 2 i$

Conclusion

The complex roots of the polynomial are 3+2i, 3-2i

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find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} - 8 x^{2} + 25 x - 26$

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)=x3-8x2+25x-26

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

Decision Maths

Mechanics Maths

Logic and Functions

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

find the complex zeros of each polynomial function. Write f in factored form
$f (x) = x^{3} - 8 x^{2} + 25 x - 26$