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December 22, 2014

December 22, 2014

Posted by **Nick** on Thursday, December 13, 2007 at 7:41pm.

I’ve used synthetic division to get the answers x = 1 +/- 2i , 1 +/- sqrt 2

I’ve having trouble checking the answers though because of that imaginary number. How can I check these kind of problems?

- Algebra II -
**Damon**, Thursday, December 13, 2007 at 8:16pmIf (-1+2i) is a solution, its complex conjugate (-1-2i) must be a solution.

In other words

x = -1+2i

x = -1-2i

are solutions

so

x+1-2iand x+1+2i are both factors

so their product should be a factor

I get x^2+2x+5

now do your division

I get

x^2-2x-1

well

that is

(x-1)(x-1)

so my four solutions are those two complex conjugates and x=1 and x =1 again

- Algebra II -
**Damon**, Thursday, December 13, 2007 at 8:28pmWhoa - a bit hasty there

x^2-2x-1

can not factor that so easily!

I will have to solve it

x^2-2x-1 = 0

x = (1/2)(2 +/-sqrt(4+4))

=(1/2)(2 +/-2sqrt(2))

x = 1+sqrt(2)

or

x = 1-sqrt(2)

are the last two solutions

- Algebra II -

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