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anonymous
 one year ago
Find a cubic function with the given zeros.
√6 , √6, 3
anonymous
 one year ago
Find a cubic function with the given zeros. √6 , √6, 3

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.2what do we know about zeros of a function, what do they do to the function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they mark the intercepts?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2yeah, they do mark the x intercepts. but something more useful to is is that the make the function, equal out to zero.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2now, another thing we should know, is that anything times 0, is equal to 0 ... right?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2so, would you agree that if x=a, then xa = 0 ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2given any number of roots, we can then create a function: say the roots are a,b,c let f(x) = (xa)(xb)(xc) will f(a)=0? f(b)=0? and f(c)=0?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so we have to find which one ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2we simply need to expand (multiply thru, distribute) this into the cubic format.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2let f(x) = (xa)(xb)(xc) for the stated zeros; a,b, and c how would we expand this into a cubic format?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2can you show me how it looks when we multiply it out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427elr1dfihajj is that right?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2that link is not working for my browser :/ (xc)(xxbxax+ba) xxxbxxaxx+bax cxx+bcx+caxabc x^3 (a+b+c)xx^2 +(ab+ac+bc)x abc

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2let a=sqrt(6), b=sqrt(6), and c=3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0btw the link says x^3 + 3x^2 6x 18

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2a+b+c = 3, so 3 = 3 is fine ab+ac+bc = 6, thats good and (6.3) is 18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now we just combine them to get the function

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2that IS the function ..

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2f(x) = x^3 +3x^26x18

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2any scaled form of this also works ... so this is not a unique solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i see, thanks so much!
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