sugagal
please help solve this F(x)= x2 -5x-36
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anonymous
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solve what? this is a function. what do you want to do with it?
sugagal
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zero of the polynomial function
sandra
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is the first term x^2?
sugagal
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yes
sandra
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ok, so you want to know what numbers multiply to get -36 but add to get -5
sugagal
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ok (x-9) and (X+4)
sandra
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so options for -36 = (-1, 36), (-2,18), (-3,12), (-6,6), (-9,4), (-12,3)... so on
sandra
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exactly!
sugagal
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thats as far as I got
sandra
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so (x-9) * (x+4) distributes to get the right side of the equation
sandra
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so what values could x have to make the factored version multiple to zero? it's whatever makes the individual factored terms "0" - since anything multiplied by zero is 0
sandra
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so the first one is (x-9) = 0 OR (x+4) = 0 - those are the roots, solve for x in each case
sandra
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in the first case, x=9, since (9-9)=0, and 0*(x+4) = 0. So 9 is one root
sandra
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what is the other one? it's the number that makes (x+4) = 0
sandra
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so you can do that =)
sugagal
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-4
sugagal
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x=-4
sandra
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exactly, so you have your two roots =). 9 and -4
sandra
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So the entire thought process is:
1. F(x)= x^2 -5x-36 - find the roots - ok so that means what values of x makes F(X)=0
2. Oh crap, that's hard to just guess and check. I better factor it.
3. F(x) = (x-9)*(x+4) //factored and equivalent
4. OK, so now it's easy to see. The function will equal zero when either (X-9) =0 , OR (x+4) =0.
5. x=9, or x=-4
sugagal
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ok, so is that the answer
sandra
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yes
sandra
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zero means "where does the function = 0". so you found both places
sugagal
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oh ok thank you very much for you help
sandra
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np good luck!