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Quadratic in different forms

  1. Dec 3, 2016 #1
    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. jcsd
  3. Dec 3, 2016 #2

    Orodruin

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    You will need to define ##\alpha## and ##\beta##. How else are we to know what they are?
     
  4. Dec 3, 2016 #3
    hint is ##(a+b)^2=6^2=a^2+b^2+2ab##
     
  5. Dec 3, 2016 #4
    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##
     
  6. Dec 3, 2016 #5
    Thanks Delta.........let me see now
     
  7. Dec 3, 2016 #6
    we have ##36=α^2+β^2+2αβ, →36=α^2+β^2+40, → α^2+β^2= -4##
     
  8. Dec 3, 2016 #7
    Greetings from Africa Chikhabi from East Afica, Kenya.
     
  9. Dec 3, 2016 #8

    haruspex

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    Yes.
     
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