#Why do other factorization methods give me slightly different result than quadratic formula

38 messages · Page 1 of 1 (latest)

outer wigeon
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the negative on the -4 in the numerator and on a cancel

hushed plume
outer wigeon
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what?

hushed plume
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I don't understand what you're refering to

outer wigeon
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both factorizations, yours and theirs have roots x=1 and x=3

hushed plume
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but if my root is x=3 then it would be (x-1)(x-3)

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not (x-1)(3-x)

outer wigeon
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3-3=0

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so x=3 is a root to that

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the quadratic had a -x^2, your factorization wouldnt

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you can write it as -(x-1)(x-3) to correct that

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and then note -(x-3)=3-x

hushed plume
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so one of the parenthesis has to be negative because of the negative x square?

outer wigeon
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yeah

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else the factorization wont give you the same expanded polynomial

hushed plume
outer wigeon
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the quad formula just tells you the roots

hushed plume
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is it always like this when the x^2's coefficient is negative?

outer wigeon
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it doesnt tell you necessarily anything about the factorization

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just that the factorization will be a(x-r)(x-s)

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for roots r and s

hushed plume
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yeha but here r is 1 and s is 3

outer wigeon
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yeah

hushed plume
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but it isnt (x-1)(x-3)

outer wigeon
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and a is -1

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not 1

hushed plume
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but the quad formula gave me 1

outer wigeon
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so the factorization is -(x-1)(x-3)

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since a=-1, r=1, s=3

hushed plume
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oh

outer wigeon
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which is ofc (x-1)(3-x)

hushed plume
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a is the x^2's coefficient?

outer wigeon
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yes

hushed plume
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I feel dumb now ty

outer wigeon
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ax^2+bx+c

hushed plume
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im learning derivatives and I still suck at factoring lmao

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so do I just delete this thread? @outer wigeon

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also ty for your help