Q. 10 In the complex number system, so... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 10 (page 556)

In the complex number system, solve the equation $3 x^{5} - 10 x^{4} + 21 x^{3} - 42 x^{2} + 36 x - 8 = 0$

Short Answer

Expert verified

The solution of the equation in the complex number system is $\{- 2 i, 2 i, 1, 2, \frac{1}{3}\} .$

Step by step solution

Step 1. Given Information

The given equation is $3 x^{5} - 10 x^{4} + 21 x^{3} - 42 x^{2} + 36 x - 8 = 0 .$

We have to solve the equation.

Step 2. Solve

$3 x^{5} - 10 x^{4} + 21 x^{3} - 42 x^{2} + 36 x - 8 = 0 (3 x^{5} + 21 x^{3} + 36 x) - (10 x^{4} + 42 x^{2} + 8) = 0 3 x (x^{4} + 7 x^{2} + 12) - 2 (5 x^{4} + 21 x^{2} + 4) = 0 3 x (x^{4} + 4 x^{2} + 3 x^{2} + 12) - 2 (5 x^{4} + 20 x^{2} + x^{2} + 4) = 0 3 x [x^{2} (x^{2} + 4) + 3 (x^{2} + 4)] - 2 [5 x^{2} (x^{2} + 4) + 1 (x^{2} + 4)] = 0$

Step 3. Solve

By proceeding with the calculation further

$3 x (x^{2} + 3) (x^{2} + 4) - 2 (5 x^{2} + 1) (x^{2} + 4) (x^{2} + 4) [3 x (x^{2} + 3) - 2 (5 x^{2} + 1)] = 0 (x^{2} + 4) (3 x^{3} + 9 x - 10 x^{2} - 2) = 0 (x^{2} + 4) (3 x^{3} - 3 x^{2} - 7 x^{2} + 9 x - 2) = 0 (x^{2} + 4) [3 x^{2} (x - 1) - (7 x^{2} - 9 x + 2)] = 0 (x^{2} + 4) [3 x^{2} (x - 1) - (7 x^{2} - 7 x - 2 x + 2)] = 0$

Step 4. Solve

By proceeding with the calculation further

$(x^{2} + 4) [3 x^{2} (x - 1) - (x - 1) (7 x - 2)] = 0 (x^{2} + 4) (x - 1) (3 x^{2} - (7 x - 2)) = 0 (x^{2} + 4) (x - 1) (3 x^{2} - 7 x + 2) = 0 (x^{2} + 4) (x - 1) (3 x^{2} - 6 x - x + 2) = 0 (x^{2} + 4) (x - 1) (x - 2) (3 x - 1) = 0$

Step 5. Writing the equation in the complex number system

As we know $(x^{2} + a^{2}) = (x + a i) (x - a i) and i^{2} = - 1 .$

Therefore,

$(x + 2 i) (x - 2 i) (x - 2) (3 x - 1) = 0$

Thus, the solution of the equation in the number system is $\{- 2 i, 2 i, 1, 2, \frac{1}{3}\} .$

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91影视

In the complex number system, solve the equation $3 x^{5} - 10 x^{4} + 21 x^{3} - 42 x^{2} + 36 x - 8 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve

Step 3. Solve

Step 4. Solve

Step 5. Writing the equation in the complex number system

One App. One Place for Learning.

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91影视

In the complex number system, solve the equation3x5-10x4+21x3-42x2+36x-8=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve

Step 3. Solve

Step 4. Solve

Step 5. Writing the equation in the complex number system

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Mechanics Maths

Applied Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In the complex number system, solve the equation $3 x^{5} - 10 x^{4} + 21 x^{3} - 42 x^{2} + 36 x - 8 = 0$