Expressing Quadratic Equations in Different Forms

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Homework Help Overview

The discussion revolves around expressing the quadratic equation \(x^2 - 6x + 20\) in different forms and finding specific values related to its roots, denoted as \(\alpha\) and \(\beta\).

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definitions of \(\alpha\) and \(\beta\) and how they relate to the quadratic equation. There are hints regarding the use of the identity \((a+b)^2 = a^2 + b^2 + 2ab\) to find \(\alpha^2 + \beta^2\). Some participants explore the relationship between the coefficients of the quadratic and the roots.

Discussion Status

Several participants have provided hints and explored different aspects of the problem, particularly focusing on the relationships between the roots and the coefficients. There is an ongoing examination of the calculations related to \(\alpha^2 + \beta^2\), with some participants expressing uncertainty about the results.

Contextual Notes

There is mention of missing reference notes, which may affect the participants' ability to fully engage with the problem. The discussion includes a mix of assumptions and interpretations regarding the values of the roots.

chwala
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Homework Statement


Express the quadratic equation ##x^2-6x+20## in the different form hence find,## 1. α+β, αβ , α^2+β^2##

Homework Equations

The Attempt at a Solution


## -(α+β)= -6 ⇒α+β= 6, αβ=20##
[/B]
now where my problem is finding ##α^2+β^2## , i don't have my reference notes here ...hint please
 
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You will need to define ##\alpha## and ##\beta##. How else are we to know what they are?
 
hint is ##(a+b)^2=6^2=a^2+b^2+2ab##
 
Ok let the roots of a qaudratic equation be ##x=α , x=β→ (x-α)(x-β)## are factors of a quadratic function thus on expanding
## x^2-(α+β)x+αβ = x^2-6x+20##
 
Thanks Delta...let me see now
 
we have ##36=α^2+β^2+2αβ, →36=α^2+β^2+40, → α^2+β^2= -4##
 
Greetings from Africa Chikhabi from East Afica, Kenya.
 
chwala said:
we have ##36=α^2+β^2+2αβ, →36=α^2+β^2+40, → α^2+β^2= -4##
Yes.
 

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