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anonymous
 5 years ago
how to find the zeros of \[x ^{3}\] + x + 10
anonymous
 5 years ago
how to find the zeros of \[x ^{3}\] + x + 10

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nikvist
 5 years ago
Best ResponseYou've already chosen the best response.0\[x^3+x+10=0\] \[(x+2)\cdot(x^22x+5)=0\] \[(x+2)\cdot((x1)^2+4)=0\] \[x_1=2\quad,\quad x_{2,3}=1\pm 2i\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but how to find the first step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well i see  something you have to get used to ^^ thanks a lot

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Neasd, you can use the 'rational root theorem' to test for rational roots.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The roots will be of the form\[\frac{p}{q}=\frac{\pm \left\{ factors.of.constant.term \right\}}{\left\{ factors.of.coefficient .of.highest.power \right\}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So here,\[\frac{p}{q}=\frac{\pm \left\{ 1,2,5,10 \right\}}{\left\{ 1 \right\}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x=\frac{p}{q}=\frac{2}{1}=2\]is one element of the set. When you test this, you find\[(2)^3+(2)+10=82+10=0\]so x=2 is a root. You can then factor \[(x(2))=(x+2)\]out of your polynomial.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know how to use long division on polynomials? That is the next step.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0long division? hm never heard of that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The aim is to find Q(x) such that\[x^3+x+10=(x+2)Q(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's a little difficult to explain on this site. I'll see if I can find a clip that will show you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a i see polynomdivision ;D my first language is german ^^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i know to do that :D thank you!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0http://www.khanacademy.org/video/polynomialdivision?playlist=ck12.org%20Algebra%201%20Examples

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The division will find the Q(x), which is the quadratic Nikvist found.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're welcome, Markus :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just want to add, if you test all the possible rational combinations and none of them satisfy the condition of a root (i.e. your polynomial does not go to zero), the polynomial has *no* rational roots (you're then left with irrational or complex).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok now i'm prepared :D thx again ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0may i ask you, what you are doing atm? student? postdoc etc? :D
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