Synthetic Division: x^4-4x^3+14x^2-4x+13=0, x=2-3i

[demclau]

How do I use synthetic division to determine that 2-3i is a solution for x^4-4x^3+14x^2-4x+13 = 0?

Thanks

 

[Deleted member 4993]

Re: Synthetic Division

How do I use synthetic division to determine that 2-3i is a solution for x^4-4x^3+14x^2-4x+13 = 0?

Thanks

Do you hafta use synthetic division??

How would you use synthetic division to determine that 2 is a solution for x[sup:2nkhigge]3[/sup:2nkhigge] - 8 = 0?

You would divide by (x-2)?

It would faster though to use f(a) = 0 when x = a is a solution f(x) = 0.

 

[demclau]

Re: Synthetic Division

Yes, I have been asked to prove this by using synthetic division.

 

[stapel]

Yes, I have been asked to prove this by using synthetic division.

For an example of how this works, try the bottom of this page. :wink:

 

[DrMike]

Rather than mess with complex numbers, I'd suggest noting that x=2-3i is a root of x[sup:14rj6354]2[/sup:14rj6354]-4x+13, then divide your original polynomial by this quadratic and note that there is no remainder.