Question:
How do I find all roots of the polynomial if 1-3i is a root?
Aron
2012-05-16 18:23:22 UTC
How do i find all roots of the polynomial if 1-3i is a root. 3x^3-13x^2+44x-70?
Also, then factor over the set of complex numbers.
Three answers:
2012-05-16 18:25:03 UTC
hint: an other root 1+3i
2012-05-16 18:32:13 UTC
Imaginary roots come in conjugate pairs, thus, if 1-3i is a root, 1+3i is also a root. Since your polynomial is to the third degree, there are 3 zeros. To find the third root, you take the roots:

[x - (1- 3i)] and [x - (1+3i)] and multiply them.



Then you divide 3x^3-13x^2+44x-70 by the product above (using polynomial long division) which should yield your final root.



Remember: A factor of a polynomial is written as (x-c), so if 7 is a zero, (x-7) is a factor.
Infinity
2012-05-16 18:30:48 UTC
1+3i is in fact another root. I also think synthetic division sounds like a grand idea! :)


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