Q. 93 One solution of the equation x3-... [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 4: Q. 93 (page 210)

One solution of the equation $x^{3} - 8 x^{2} + 16 x - 3 = 0$ is $3$ .
Find the sum of the remaining solutions.

Short Answer

Expert verified

If $3$ is a solution of the equation $x^{3} - 8 x^{2} + 16 x - 3 = 0$ then the sum of remaining solutions will be $5$

Step by step solution

Step 1. given data

The given equation is

$x^{3} - 8 x^{2} + 16 x - 3 = 0$

one solution of the equation is $3$

Step 2. factorize the equation

one solution of the equation is $x = 3$

divide the expressionlocalid="1646068985153" $x^{3} - 8 x^{2} + 16 x - 3$ by $x - 3$

localid="1646070020448" $\frac{x - 3 \begin{matrix} x^{2} - 5 x + 1 \end{matrix} \begin{matrix} x^{3} - 8 x^{2} + 16 x - 3 \\ - (x^{3} - 3 x^{2}) \end{matrix}}{\frac{\begin{matrix} - 5 x^{2} + 16 x - 3 \\ - (- 5 x^{2} + 15 x) \end{matrix}}{\frac{\begin{matrix} x - 3 \\ - (x - 3) \end{matrix}}{0}}}$

so the equation can be factorized aslocalid="1646070164973" $(x - 3) (x^{2} - 5 x + 1) = 0$

Step 3. Apply the quadratic formula

use the quadratic formula to find the solution of $(x^{2} - 5 x + 1)$

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- (- 5) 卤 \sqrt{{(- 5)}^{2} - 4 (1) (1)}}{2 (1)} x = \frac{5 卤 \sqrt{21}}{2} x = \frac{5 + \sqrt{21}}{2}, \frac{5 - \sqrt{21}}{2}$

Step 4. the sum of solutions

Sum of solutions of the equation except $x = 3$

$\frac{5 + \sqrt{21}}{2} + \frac{5 - \sqrt{21}}{2} = \frac{5 + \sqrt{21} + 5 - \sqrt{21}}{2} = \frac{10}{2} = 5$

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91影视

One solution of the equation $x^{3} - 8 x^{2} + 16 x - 3 = 0$ is $3$ .
Find the sum of the remaining solutions.

Short Answer

Step by step solution

Step 1. given data

Step 2. factorize the equation

Step 3. Apply the quadratic formula

Step 4. the sum of solutions

One App. One Place for Learning.

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91影视

One solution of the equation x3-8x2+16x-3=0 is 3.Find the sum of the remaining solutions.

Short Answer

Step by step solution

Step 1. given data

Step 2. factorize the equation

Step 3. Apply the quadratic formula

Step 4. the sum of solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Decision Maths

Logic and Functions

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

One solution of the equation $x^{3} - 8 x^{2} + 16 x - 3 = 0$ is $3$ .
Find the sum of the remaining solutions.