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.