Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Mathematical Problem: Solving a Quadratic Equation**
**Problem Statement:**
Solve for \( x \).
\[ R x^2 + T x + Q = 0 \]
This problem involves solving a quadratic equation in the standard form, where \( R \), \( T \), and \( Q \) are constants, and \( x \) is the variable.
To solve this equation, you can use the quadratic formula:
\[ x = \frac{-T \pm \sqrt{T^2 - 4RQ}}{2R} \]
For real solutions, the discriminant (\( T^2 - 4RQ \)) must be non-negative. Depending on the values of the discriminant:
- If \( T^2 - 4RQ > 0 \), there are two distinct real solutions.
- If \( T^2 - 4RQ = 0 \), there is exactly one real solution (a repeated root).
- If \( T^2 - 4RQ < 0 \), there are no real solutions; instead, there are two complex solutions.
The quadratic formula and the evaluation of the discriminant provide a comprehensive method for solving any quadratic equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F189b1028-a7d5-4a13-b58d-f60d7c89225b%2Fbc7ab3de-27e5-4364-91e9-7db4eb7c7a63%2Frxy8lad.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematical Problem: Solving a Quadratic Equation**
**Problem Statement:**
Solve for \( x \).
\[ R x^2 + T x + Q = 0 \]
This problem involves solving a quadratic equation in the standard form, where \( R \), \( T \), and \( Q \) are constants, and \( x \) is the variable.
To solve this equation, you can use the quadratic formula:
\[ x = \frac{-T \pm \sqrt{T^2 - 4RQ}}{2R} \]
For real solutions, the discriminant (\( T^2 - 4RQ \)) must be non-negative. Depending on the values of the discriminant:
- If \( T^2 - 4RQ > 0 \), there are two distinct real solutions.
- If \( T^2 - 4RQ = 0 \), there is exactly one real solution (a repeated root).
- If \( T^2 - 4RQ < 0 \), there are no real solutions; instead, there are two complex solutions.
The quadratic formula and the evaluation of the discriminant provide a comprehensive method for solving any quadratic equation.
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