Expressing Quadratic Equations in Different Forms

[chwala]

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

 

[Orodruin]

You will need to define ##\alpha## and ##\beta##. How else are we to know what they are?

 

[Delta2]

hint is ##(a+b)^2=6^2=a^2+b^2+2ab##

 

[chwala]

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##

 

[chwala]

Thanks Delta...let me see now

 

[chwala]

we have ##36=α^2+β^2+2αβ, →36=α^2+β^2+40, → α^2+β^2= -4##

 

[chwala]

Greetings from Africa Chikhabi from East Afica, Kenya.

 

[haruspex]

we have ##36=α^2+β^2+2αβ, →36=α^2+β^2+40, → α^2+β^2= -4##

Yes.