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  1. D

    How to solve this?

    Cherry Finally found my LaTeX error for my solution to e) above.
  2. D

    How to solve this?

    For e): \therefore $ sum of roots: $ \frac {1}{k}\alpha + \alpha + k\alpha = - b \implies (\frac {1}{k} + 1 + k)\alpha = -b \\ \\ $ sum of root pairs: $ \frac {1}{k} \alpha \times \alpha + \frac {1}{k} \alpha \times k \alpha + \alpha \times k \alpha = (\frac {1}{k} + 1 + k)\alpha ^2 = c...
  3. D

    How to solve this?

    For c): P(x) = x^3 + 4x^2 + 2x + k You are told: remainder upon division by (x-1) = 2 times remainder upon division by x or (x-0). That means P(1) = 2 P(0) i.e. 1 + 4 + 2 + k = 2 x k .: k = 7
  4. D

    How to solve this?

    Cherry: I know you want a very gentle step-by-step help. Not helpful hints here and there. For b) P(x) = (x^2-1)Q(x) + kx + 2 If x-1 is a factor of P(x), then the Remainder Thm tells you that P(1) = 0 i.e. P(1) = (1^2 - 1)Q(1) + k + 2 = 0 ==> 0 + k + 2 = 0 so that k = -2. You now know that...
  5. D

    How to solve this?

    Or doing the usual way: \frac {2x(x-4)}{(x-1)} > 7\\ \\ \therefore (x-1)^2\times \left [ \frac {2x(x-4)}{(x-1)}\right ] > (x-1)^2 \times 7 \\ \\ \therefore 2x(x-4)(x-1) > 7(x-1)^2\\ \ \therefore (x-1)[2x(x-4) - 7(x-1) > 0] \\ \\ \therefore (x-1)(2x^2-15x+8) > 0 \\ \\ \therefore (x-1)(2x-1)(x-7)...
  6. D

    How to solve this?

    If question is to solve, say: \frac {2x(x-4)}{x-1} > 7 can do this in a number of ways. One is using sign diagrams. Note because of the denominator, note x must not equal 1. The above inequality is equivalent to: \frac{(2x - 1)(x-7)}{(x-1)} > 0 3 relevant factors are: 2x-1, x-7 and x-1...
  7. D

    How to solve this?

    Don't understand your question. What is that small circle??
  8. D

    Should I apply to Ruse?

    Just pulling your leg.
  9. D

    Should I apply to Ruse?

    When you say you are pretty all rounded, does it mean you are rotund?
  10. D

    induction question

    Love your very nice handwriting too, harrowed2.
  11. D

    HOW DO YOU IMPROVE CHEMISTRY!!!

    It looks like you are unable to "get it" by yourself. So you will need someone to help you, if you can be helped at all. Going to a Chemistry coaching centre isn't the place for you. You will need someone, like jazz519, to give you personalised help. Getting a "right person" to help you is very...
  12. D

    To all the people who have done the hsc or are in year 12 right now...

    Lots of people seek advice. Say just a few things about their problem. Do we really have enough background info about you to give you meaningful advice?
  13. D

    Math1131

    One suggestion: In the end-of-school-term Lifeline book sales, you can often pick up a good uni 1st year American Calculus text book - usually for less than $10. (I once picked up an unused hardcover university text with about 1000 pages: Physics - by Young & Freedman for only $2!). This...
  14. D

    IB Maths Tutor - Sydney

    Bump
  15. D

    Binomial Theorem Questions

    Sorry - didn't read your full post!
  16. D

    Binomial Theorem Questions

    Use fact: coeff of term in x^n of LHS = coeff of term in x^n of RHS and note fact that nCr = nCn-r.
  17. D

    2nd Year Engineering Maths ODE's

    If so: xlny\frac{dy}{dx} = 3x^2y \\ \\ \therefore lny \frac{dy}{dx} = 3xy \\ \\\frac{lny}{y}dy = 3xdx \\ \\ \therefore \int \frac{lny}{y} dy = \int 3xdx \\ \\ \frac{1}{2} (lny)^2 = \frac{3x^2}{2} + \frac{C}{2}\\ \\ (lny)^2 = 3x^2 + C \\ \\ lny = \pm\sqrt{3x^2+C}\\ \\ \therefore y = e^{\pm...
  18. D

    Should I drop to Standard Math??

    Why are you doing Physics if you don't even like maths? You will be handicapped in your Physics, even if it has been mathematically diluted.
  19. D

    Making notes advice

    Tiring, but maybe in the long run, helpful.
  20. D

    Handwriting

    Cujo10 has little choice, unless, somehow miraculously he can learn to write. I've tried to help quite a few individuals over the years with their handwriting but unfortunately the results are not very good.
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