HSC Stuff > HSC Mathematics Extension 2
4U Maths Question Thread
jakesilove:
--- Quote from: jamonwindeyer on February 11, 2016, 11:23:01 pm ---Hey xXCandyDXx! Glad Jake could be of help!
In addition, a tip for spotting when to use the "sums of roots" formulae. Pretty much, if a question follows the following template:
Find the roots of ____________________ given that __________________
or even
The roots of ___________________ form an arithmetic series. Find the value of k (some unknown in the polynomial))
Essentially, if you are given a polynomial with something to find, and all you are given is some information about the roots, chances are that these formulae will help you. They are very powerful in surprising ways.
While I'm here, I have an issue with the method you posted above. It's very possible I am misunderstanding, but it seems like the notions of root and factor are being confused. Remember, factors can be multiplied together to get back to the original, roots are just solutions to the polynomial equal to zero.
So, in the first few lines, we multiply the roots together and then form an identity with the original polynomial. This doesn't make sense to me. We could do it with factors, but multiplying the roots of a polynomial together has no relationship with the original, besides the relationships highlighted in the formulae used by Jake's method.
The factor rule makes perfect sense. The first part of the solution however, while the correct answer is obtained, does not make as much sense to me, and I would argue that it is incorrect. I'd love to hear others interpretations on the matter! ;D
--- End quote ---
Hey Jamon!
Thanks for clarifying when to use the sum and product formulas for Polynomial questions!
Also, I agree that her method is actually incorrect, but as luck would have it gets to the right answer. Here's why
Jake
Happy Physics Land:
--- Quote from: jakesilove on February 12, 2016, 09:36:28 am ---Hey Jamon!
Thanks for clarifying when to use the sum and product formulas for Polynomial questions!
Also, I agree that her method is actually incorrect, but as luck would have it gets to the right answer. Here's why
(Image removed from quote.)
Jake
--- End quote ---
Jake you are such a god what an elaborative response!
Happy Physics Land:
Please send help Almighty Jake when you are available!!! This has been screwing me over!!! :-[
Thank you so much Jake! <3 (I dont know why the images are sideways doe...)
xXCandyDXx:
Sorry for the very late response!!! >~<
Thanks Jamon and Jake for clearing it up ... I guess it is luck that I got the answer this time hehe ... But YEP thank you guys! I understand a lot more about polynomials and how they work .. Kinda HAHA I'm getting there! But i totally get where you're coming from in the sense that I suddenly multiplied the roots and equated them ...( clearly I don't understand ) but yeah I was actually thinking of trying to multiply the factors together which I totally mistook ... for the roots ahh... But yeah !!! Thanks again !!! I won't be making the same mistake in the future for sure
xXCandyDXx:
--- Quote from: Happy Physics Land on February 12, 2016, 11:15:56 am ---
Jake you are such a god what an elaborative response!
--- End quote ---
He really is a god
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