Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![### Verification of Solutions to a Quadratic Equation by Substitution
In this exercise, you are asked to verify by substitution that the given values of \(x\) are solutions to the given quadratic equation:
\[ x^2 - 6x + 16 = 0 \]
The proposed solutions are:
\[ (a) \, x = 3 + i\sqrt{7} \]
\[ (b) \, x = 3 - i\sqrt{7} \]
You will need to verify each proposed solution by substituting the value of \(x\) back into the original equation.
#### Interactive Component:
- **Part: 0 / 4** (Progress bar indicating current score out of a total of 4 points)
#### Instruction for Part 1 of 4:
- **(a) Substituting the given value for \(x\) makes the equation (Choose one) \(\_\_\_\).**
- Here, you need to select from a dropdown menu indicating whether the substitution is correct or not.
- You will then confirm your selection by clicking the submit button (which is symbolized by a checkmark within a square box).
This exercise will help solidify your understanding of solving and verifying quadratic equations using complex numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd02c2397-8a4d-4107-81f2-96f803d8dc68%2Fe84d3aa5-643d-4ce8-afca-2ddc7faeea21%2Fdtx2lz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Verification of Solutions to a Quadratic Equation by Substitution
In this exercise, you are asked to verify by substitution that the given values of \(x\) are solutions to the given quadratic equation:
\[ x^2 - 6x + 16 = 0 \]
The proposed solutions are:
\[ (a) \, x = 3 + i\sqrt{7} \]
\[ (b) \, x = 3 - i\sqrt{7} \]
You will need to verify each proposed solution by substituting the value of \(x\) back into the original equation.
#### Interactive Component:
- **Part: 0 / 4** (Progress bar indicating current score out of a total of 4 points)
#### Instruction for Part 1 of 4:
- **(a) Substituting the given value for \(x\) makes the equation (Choose one) \(\_\_\_\).**
- Here, you need to select from a dropdown menu indicating whether the substitution is correct or not.
- You will then confirm your selection by clicking the submit button (which is symbolized by a checkmark within a square box).
This exercise will help solidify your understanding of solving and verifying quadratic equations using complex numbers.
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