#Partition analysis

22 messages · Page 1 of 1 (latest)

molten sonnet
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Amount analysis x^4-13x^2+36

distant lodgeBOT
cursive fulcrum
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So you want to have this in its linear factors, right?

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In this case you transform the function into another. ( Works because this is a biquadratic function), so instead of x⁴-13x²+36 you have z²-13z+36 ( any variable, I just used z), and bang you have a quadratic function. So what do we need for linear factors? The zeros, so now you have z²-13z+36 = 0. You know what to do here? ||If not search up either pq formula or midnight formula, don't know which one you use at school||. After you got your z's so that f(z) = 0, you have to check if they are all positive,
because z = x², so to get x you need the quadraticroot of this ( and I am pretty sure you use real numbers) and we all know we can't do that with real numbers. So cross all negative zs out and take the quadraticroot of the other one, always remember two possible answers, one positive and one negative.

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Summarised

  1. Step: define z = x² and use z with the koeffiziens before the x's.
  2. Step: get the zeros for the z's
  3. Step: transform the z's into x's through the quadraticroot of them
  4. Step: because we want the linear factors we just have to write (x + n)(x + p) (x + q) ( x + r) they are just random variables for the real zeros in no specific order.
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Hope, I could be of any help and didn't misinterpret the task

sage robin
rotund monolith
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Just do rational root theorem

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Find the factor of 36 over the factor of 1

molten sonnet
cursive fulcrum
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Because I absolutely have no idea what you mean, because this question doesn't occur to me, the function has as the highest exponent a four ( crazy I know) , so neither directly quadratic and surely not cubic, or do you want to know if the zeros are double, or triple and so? (I don't think so, but if yes , no they are all normal ones). If I am to be wrong, execute me. Also because I possess no hobbies we dare speak of ||(x-3)(x+3)(x-2)(x-2), would be the answer, and yes I did calculate all of this in my head ||, also only check if you already have a solution, no cheating under my watch. ( May your conscience hinder you), I should have written this before hand, I know.
Really explain your question further if I am expected to understand, I am really struggling to interpret that. (Main reason may be my foreignness with the English language and the problem of having not used that term. After searching up these terms, I realised, yes my first assumption was right, and to say it is neither quadratic nor cubic analysis. And that you can use the way I described before hand.

rotund monolith
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18 possible solutions

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If you have Desmos graph it

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If not try each solutions

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Using synthetic division

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Until their remainder is 0

molten sonnet
molten sonnet
rotund monolith
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Huh

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I used desmos to get plus or minus 2 and 3

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This case ima use -2, and -3