Question 1154863: my first period algebra class has been working on polynomials for quite a while, i'm struggling to understand the topic, but have some sort of understanding of a few things inside the topic. so the problem i'm asking for help with looks like this;
given a polynomial has roots at -4 and 2i, find a third degree polynomial equation that would pass through these roots.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not exactly sure, but i think it works like this.
if x = -4, then x + 4 = 0
if x = 2i, then x - 2i = 0
complex roots always work in pairs, therefore you also have x + 2i = 0
your third degree equation will be (x + 4) * (x - 2i) * (x + 2i).
when x = -4, this equation becomes (-4 + 4) * (-4 - 2i) * (-4 + 2i) = 0
this is because (-4 + 4) = 0.
when x = 2i, this equation becomes (2i + 4) * (2i - 2i) * (2i + 2i) = 0
this is because (2i - 2i) = 0.
the roots are when y = 0.
the equation is y = (x + 4) * (x - 2i) * (x + 2i).
when y = 0, the equation becomes (x + 4) * (x - 2i) * (x + 2i) = 0].
if you simplify the equation, it becomes x^3 + 4x^2 + 4x + 16 = 0.
here's a reference that addresses polynomials and polynomial functions.
https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm
here's a more advance reference from the same folks.
https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm
i found both these references very helpful when i was brushing up on my math.
in the first reference, look for tutorials 25 through 30 (intermediate algebra).
in the second reference look for tutorials 34 through 40 (college algebra).
feel free to go through the other tutorials as well.
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