Find a cubic function with the given zeros. √6 , -√6, -3

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Find a cubic function with the given zeros. √6 , -√6, -3

Mathematics
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what do we know about zeros of a function, what do they do to the function?
they mark the intercepts?

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yeah, they do mark the x intercepts. but something more useful to is is that the make the function, equal out to zero.
now, another thing we should know, is that anything times 0, is equal to 0 ... right?
yep
so, would you agree that if x=a, then x-a = 0 ?
yes
given any number of roots, we can then create a function: say the roots are a,b,c let f(x) = (x-a)(x-b)(x-c) will f(a)=0? f(b)=0? and f(c)=0?
okay, so we have to find which one ?
we simply need to expand (multiply thru, distribute) this into the cubic format.
let f(x) = (x-a)(x-b)(x-c) for the stated zeros; a,b, and c how would we expand this into a cubic format?
multiply it out
can you show me how it looks when we multiply it out?
http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427elr1dfihajj is that right?
that link is not working for my browser :/ (x-c)(xx-bx-ax+ba) xxx-bxx-axx+bax -cxx+bcx+cax-abc x^3 -(a+b+c)xx^2 +(ab+ac+bc)x -abc
let a=sqrt(6), b=-sqrt(6), and c=-3
ok
btw the link says x^3 + 3x^2 -6x -18
a+b+c = -3, so --3 = 3 is fine ab+ac+bc = -6, thats good and -(--6.3) is -18
so now we just combine them to get the function
that IS the function ..
f(x) = x^3 +3x^2-6x-18
any scaled form of this also works ... so this is not a unique solution
i see, thanks so much!
goodluck

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