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anonymous

  • one year ago

Factor x2 - 2x + 3

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  1. aric200
    • one year ago
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    Do you mean Factor x^2 - 2x + 3

  2. UsukiDoll
    • one year ago
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    @aric200 yes that's got to be the equation

  3. UsukiDoll
    • one year ago
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    anyway , to factor we focus on the middle term and the last term first then the sign patterns of the equation

  4. anonymous
    • one year ago
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    @aric200 yes sir

  5. UsukiDoll
    • one year ago
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    so the last term we have is a 3 and there is only one combination which is 1 x 3 = 3 so now let's grab the middle term. We notice that there is a -2 so our 1 must be positive and our 3 must be negative 1-3 = -2

  6. aric200
    • one year ago
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    It bothers me when people do not put the ^Carrots.

  7. UsukiDoll
    • one year ago
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    or am I reading this too fast? wait... I'm using discriminant formula

  8. UsukiDoll
    • one year ago
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    (-2)^2-4(1)(3) 4-12 = -8 oh nice.. we can't factor this -_- quadratic formula time

  9. UsukiDoll
    • one year ago
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    \[\frac{-b \pm \sqrt{b^2-4ac} }{2a} \]

  10. UsukiDoll
    • one year ago
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    so with the discriminant formula we already figured out the square root portion which was -8, so we let a = 1 b = -2 and c = 3 because our equation \[x^2-2x+3\] in the form of the standard quadratic equation which is \[ax^2+bx+c\]

  11. UsukiDoll
    • one year ago
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    now we just plug in our data \[\frac{2 \pm \sqrt{-8} }{2}\]

  12. UsukiDoll
    • one year ago
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    but we are not done... we can split that 8 up and negatives aren't allowed in the radicals which means we are going to get an imaginary or i out of this

  13. UsukiDoll
    • one year ago
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    \[\frac{2 \pm 2\sqrt{2}i }{2}\]

  14. UsukiDoll
    • one year ago
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    now we can get split this up and get rid of the 2's

  15. UsukiDoll
    • one year ago
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    \[\frac{2+2 \sqrt{2}i}{2}, \frac{2-2 \sqrt{2}i}{2}\]

  16. UsukiDoll
    • one year ago
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    \[1+\sqrt{2}i, 1-\sqrt{2}i\]

  17. UsukiDoll
    • one year ago
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    which is our roots..

  18. anonymous
    • one year ago
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    @UsukiDoll so thats it?!

  19. UsukiDoll
    • one year ago
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    I think it should look like this? not sure \[(x-(1+\sqrt{2}i))(x-(1-\sqrt{2}i) )\]

  20. UsukiDoll
    • one year ago
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    @ganeshie8 I'm missing something in here...aren't I?

  21. UsukiDoll
    • one year ago
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    it's just that when I use to do those problems, all of my professors care about are the roots and I didn't have to put it back into factored form like what I just typed.

  22. ganeshie8
    • one year ago
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    yeah the given quadratic cannot be factored over integers, it is prime

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