Can you please explain how to factorize

  • Thread starter sarah786
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  • #1
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Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
 

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  • #2
I like Serena
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Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
Which complex roots did you get?
 
  • #3
Mentallic
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Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
When it says factorize over the reals, it means your factors have to have real coefficients. A root of x-(a+bi) does not have all real coefficients. Also remember that any real quadratic with a complex root also has a complex conjugate as its other root. So you can also work backwards from the two conjugates to find the real quadratic that has those roots.
 
  • #4
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your equation can be written as
X4 + 6X2 - 4X2 + 9
= X4 + 6X2+9 - 4X2
= ( X2 + 3 )2 - (2X)2
= ( X2+3+2X) (X2+3- 2X)
 
Last edited:
  • #5
mathman
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Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
Let u=x2. Then you need to solve u2 +2u +9, and take square roots of both solutions.
 

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