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sasogeek

  • 2 years ago

prove that the sum S and the product P of the quadratic equation \(ax^2+bx+c=0 \) are \(S= - \frac{b}{a} \) and \(P = \frac{c}{a} \)

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  1. hartnn
    • 2 years ago
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    u can use formula , right ?

  2. hartnn
    • 2 years ago
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    \(\huge{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)

  3. sasogeek
    • 2 years ago
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    so i know that a quadratic equation is x^2+x(sum of roots)+product of roots and you can have \(\large x^2+\frac{b}{a}+\frac{c}{a} \) where from the negative with respect to the middle term....?

  4. sasogeek
    • 2 years ago
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    and idk if i can use a formula... it wasn't stated. the question is just as i asked.

  5. hartnn
    • 2 years ago
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    \(\(\huge{x_1=\frac{-b + \sqrt{b^2-4ac}}{2a}}\\\(\huge{x_2=\frac{-b - \sqrt{b^2-4ac}}{2a}}\)\)\) find x1+x2 and x1.x2

  6. sasogeek
    • 2 years ago
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    ummm sorry, \(\huge x^2+\frac{b}{a}x+\frac{c}{a}\)

  7. jiteshmeghwal9
    • 2 years ago
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    http://openstudy.com/users/jiteshmeghwal9#/updates/500b81fce4b0549a892fa59c May this tutorial help you @sasogeek :)

  8. jiteshmeghwal9
    • 2 years ago
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    u acn find some tips by using this tutorial

  9. sasogeek
    • 2 years ago
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    @hartnn that's a lot of work lol

  10. hartnn
    • 2 years ago
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    trust me, it isn't, simplification happens lot easily.....

  11. sasogeek
    • 2 years ago
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    ok i'll try :)

  12. jiteshmeghwal9
    • 2 years ago
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    \[\huge{\frac{-b + \sqrt{b^2-4ac}}{2a}+\frac{-b - \sqrt{b^2-4ac}}{2a}}\]take the denominator common\[\LARGE{\frac{(-b+\sqrt{b^2-4ac})+(-b-\sqrt{b^2-4ac})}{2a}}\]

  13. jiteshmeghwal9
    • 2 years ago
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    now by opening brackets u can solve :)

  14. hartnn
    • 2 years ago
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    for product, u'll need this : \(\huge \color{red}{(a+b)(a-b)=a^2-b^2}\)

  15. sasogeek
    • 2 years ago
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    the radicals go to 0 and you get -2b/2a .... right?

  16. hartnn
    • 2 years ago
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    yes.

  17. hartnn
    • 2 years ago
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    wasn't that simple ?

  18. hartnn
    • 2 years ago
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    'so i know that a quadratic equation is x^2+x(sum of roots)+product of roots' <---NO 'so i know that a quadratic equation is x^2-x(sum of roots)+product of roots'<---YES

  19. hartnn
    • 2 years ago
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    did u get the product ?

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