Using quadratic zeroes to find value of parameter

Click For Summary
SUMMARY

The discussion focuses on using quadratic equations to determine the values of parameters \(\alpha\) and \(\beta\) in relation to \(p\) and \(q\). The equations presented are \(\alpha^2 - p\alpha + r = \frac{\alpha^2}{4} - q\frac{\alpha}{2} + r\) and \(\beta^2 - p\beta + r = 4\beta^2 - 2q\beta + r\). Participants are encouraged to solve these equations for non-zero values of \(\alpha\) and \(\beta\) to derive insights into the relationships between the parameters. The discussion emphasizes the importance of understanding the roots of quadratic equations in parameter estimation.

PREREQUISITES
  • Understanding of quadratic equations and their properties
  • Familiarity with algebraic manipulation techniques
  • Knowledge of parameter estimation in mathematical modeling
  • Basic proficiency in solving polynomial equations
NEXT STEPS
  • Explore the derivation of quadratic formula solutions
  • Study the implications of parameter estimation in statistical models
  • Learn about the role of discriminants in determining the nature of roots
  • Investigate applications of quadratic equations in real-world scenarios
USEFUL FOR

Mathematicians, students studying algebra, and professionals involved in statistical modeling or data analysis will benefit from this discussion.

Mathsonfire
Messages
11
Reaction score
0
https://uploads.tapatalk-cdn.com/20180712/28a4bbb89e76d3478ae2fd0825562148.jpg
Question 81
 
Mathematics news on Phys.org
Re: Help

Do you have any thoughts on how to begin?
 
Since there's been no reply, let's get started by observing that we must have:

$$r=\alpha\beta$$

Now, to express \(\alpha\) and \(\beta\) in terms of \(p\) and \(q\) I would look at:

$$\alpha^2-p\alpha+r=\frac{\alpha^2}{4}-q\frac{\alpha}{2}+r$$

$$\beta^2-p\beta+r=4\beta^2-2q\beta+r$$

Solve the first equation for the non-zero value of \(\alpha\) and solve the second equation for the non-zero value of \(\beta\)...what do you find?
 

Similar threads

MHB How to Understand the Ratio of Quadratic Roots?
  • · Replies 3 ·
Replies
3
Views
1K
MHB Sum and product of roots of quadratic equation
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Do Vieta's Formulas Apply to Cubic Polynomial Roots?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Factorisation of a^2(b^3−c^3)+b^2(c^3−a^3)+c^2(a^3−b^3)
  • · Replies 10 ·
Replies
10
Views
3K
MHB Finding Coordinates of Point B - Positional Vectors
  • · Replies 8 ·
Replies
8
Views
2K
MHB The Minimum Value of a Quadratic Function: A Question of Symmetry
  • · Replies 3 ·
Replies
3
Views
2K
High School Quadratic with simple meaningful intuitive constants
  • · Replies 2 ·
Replies
2
Views
2K
High School Need assistance with an unusual quadratic solution method
  • · Replies 4 ·
Replies
4
Views
1K
MHB Probability of Spin Resulting in Even # or <4
  • · Replies 2 ·
Replies
2
Views
2K
MHB Quadratic equations intersaction point is minimum instead of roots
  • · Replies 2 ·
Replies
2
Views
1K