1. Dec 3, 2016

chwala

1. The problem statement, all variables and given/known data
Express the quadratic equation $x^2-6x+20$ in the different form hence find,$1. α+β, αβ , α^2+β^2$

2. Relevant equations

3. The attempt at a solution
$-(α+β)= -6 ⇒α+β= 6, αβ=20$

now where my problem is finding $α^2+β^2$ , i dont have my reference notes here ...hint please

2. Dec 3, 2016

Orodruin

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

3. Dec 3, 2016

Delta²

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

4. Dec 3, 2016

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
$x^2-(α+β)x+αβ = x^2-6x+20$

5. Dec 3, 2016

chwala

Thanks Delta.........let me see now

6. Dec 3, 2016

chwala

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

7. Dec 3, 2016

chwala

Greetings from Africa Chikhabi from East Afica, Kenya.

8. Dec 3, 2016

Yes.