Can you please explain how to factorize

[sarah786]

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)

 

[I like Serena]

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?

 

[Mentallic]

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.

 

[reddvoid]

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)

 

[mathman]

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.