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    Integration via Substitution

    Thanks so much Hermes1! :D appreciate it!
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    Integration via Substitution

    Wondering if some kind person could help a little with this difficult integral question. Thanks! Use{\hspace{1 mm}}the{\hspace{1 mm}}substitution\hspace{1 mm} u=x-\frac{1}{x}\hspace{1 mm}to \hspace{1 mm}show \int_{1}^{\frac{\sqrt{6}+\sqrt{2}}{2}}\frac{1+x^{2}}{1+x^{4}}dx=\frac{\pi }{4\sqrt{2}}
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    Polynomial Identities formed from roots

    Thanks heaps!
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    Polynomial Identities formed from roots

    "If one root of the polynomial x^3-bx^2+cx-d=0 is equal to the product of the other two, show that (c+d)^2=d(b+1)^2 " Btw this is question 16)a) from Year 12 Cambridge extension 1, exercise 4f
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    Deriving Motion Equations

    What equations must be derived and not memorised in motion topic?
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    Integrals resulting in Logarithms

    Even for functions such as ln sinx etc?
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    Integrals resulting in Logarithms

    Okay thanks.
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    Integrals resulting in Logarithms

    With integrals resulting in logarithmic functions, when should it be necessary to use absolute values? EG: integrating 1/x = ln IxI or lnx ?
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    Worked Solution for Cambridge Ext 2 book?

    This new curriculum, any idea what it affects in Maths Ext 2? I may be possible doing Extension 2 next year whilst completing the entirety of Extension 1 this year.
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    Thanks for the rep? Dont actually understand how the rep system works though :D

    Thanks for the rep? Dont actually understand how the rep system works though :D
    • ADrew
    • Profile post
  13. A

    The Quadratic Function and Sum/Product of roots:

    Thanks so much guys. I understand what I was doing wrong now.
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    The Quadratic Function and Sum/Product of roots:

    Used to know how to do these but I forgot as it was ages ago when I first learnt it. Was wondering if someone would kindly point me in the right direction: "Given that A and B are the roots of (2m-1)x^2+(m+1)x+1=0, find m if:" a) A=2 b) A+B=2AB AND "If one zero of y=x^2+mx+n is the...
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    Polynomial Theory Of Roots

    Thanks for helping!
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    Polynomial Theory Of Roots

    yes thanks. I now understand what to do when given one or two zeroes, but what do you do when you know no zeroes and they are not integers?
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    Polynomial Theory Of Roots

    Okay having trouble with this Q: New senior maths 3 unit exercise 27 d Q 17: "Solve the equation 6x^4-11x^3-26x^2+22x+24=0 given that the product of two roots is equal to the product of the other two"
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    Polynomial Theory Of Roots

    Given a polynomial equation and one or two roots, how does one successfully find the other two or three roots? (depending on either a cubic or quartic equation). I always end up with irrational roots when the question clearly says integer roots. What is the best way to solve an equation using...
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    Series Question Fitzpatrick 2U

    Anyway, considering I have no issues with harder topics such as calculus, etc, and I already know alot of the four unit content, it's just series and sequences that's an issue for me.
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    Series Question Fitzpatrick 2U

    LOL, I know, but it was easy once I realised what to do. Thanks, I figured it out.
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    Series Question Fitzpatrick 2U

    Please disregard this thread as I have figured out the question.
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    Series Question Fitzpatrick 2U

    No I was just posting this now, not necessarily working questions.
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