1. T

    Factorising Cubics

    I have asked way too many questions, and Im really sorry if I have bothered you lot too much, but thanks so much for the help I do apprieceate every single comment, and it is a great help to my studies. (Worried) Just a question regarding cubics, I need to factorise x^3-kx^2+2kx-k-1, I...
  2. T

    Algebra with cubics

    Ok im studying for a maths exam and there is one equation i cant do.. If a factor of P(x)=-7+ax+5x^2+15x^3+bx^4 is (x^2-1) find the values of a and b? here is the answer i cant work out how to do it :) any help is appreciated thanks answer: a= -15 b= 2 thanks Tarik (Happy)
  3. S

    Sketching Repricocals and Cubics Help

    Could someone guide me slowly through these questions please. I have no idea of how to answer them. These kind of questions are my main stumbling block in Maths. Thanks in advance !
  4. T

    factorising cubics

    is there any formula or neat trick to factorise a cubic equation like x^3 + 4x^2 -28x + 32=0?
  5. T

    Cubics in the form y= (x-h)^3+k

    a) what is the geometrical significance of h and k in y= (x-h)^3+k. Use technology to assist you to draw sketch graphs of your choice by varying values of h and k.
  6. T

    cubics in the form y= (x-h)^3

    Task 3: a) use technology to assist you to draw sketch graphs for y=(x-h)^3 when h=0,1,3,-2,-4 b) What is the geometrical significance of h in y=(x-h)^3
  7. T


    Task 2: Cubics in the form y=x^3 + k a) use technology to assist you to draw sketch graphs for y =x^3 + k when k=0,1,3,-2,-4 b)what is the geometrical significance of k in y=x^3+k ?
  8. T


    Task 1: Cubics in the form y=ax^3 a) use technology to assist you to draw sketch graphs for y=ax^3 when a= 1,-1,3,-4, 1/2, -1/3 b) what is the geometrical significance of a in y=ax^3? (comment on the sign and size of a)
  9. U


    Prove that for a cubic of the form a(x-b)^3+d then there exists at least one set of real solutions \{a,b,d\} such that: y_1=a(x_1-b)^3+d y_2=a(x_2-b)^3+d y'_1 = 3a(x_1-b)^2
  10. H

    finding roots of cubics and quartics

    How can I find the roots of these equations. I.E, how can I factor the cubic to get a binomial and a quadratic so then I can use the quad. formula for the last two factors? TYIA 10x^3-x^2+5x+4=0 also 3x^4+2x^3+7x^2+8x-20=0
  11. pickslides

    family of cubics question

    Q1. Find the equation of the form y=a(x-h)^3+k using the coordinates (0,0),(24,9) and (60,10) where (24,9) is the point of inflection. It seems obvious that using (24,9) as the point of inflection gives y=a(x-24)^3+9. Now substituting in (60,10) to find the dialation factor 'a'...
  12. G

    factorising cubics

    Can someone please explain to me the steps slowly how to factorise cubics?? The question is Factorise (s^2 - 3s + 2)(s+4) And the answer is (s-1)(s-2)(s-4) I just don't get how they got from the first step to the last step.. Here's what I tried to do... s^3 + 4s^2 -3s^2 -12s + 2s +8 s^3 +...
  13. A

    Factoring cubics

    I think that's what it's called, but, please can someone give me good instructions on how in the world I am supposed to do this problems and problems similar. 24x^3+18x^2
  14. R


    consider the equations of the cubic function and the straight line. y=x^3-x, y=ax+a The straight line crosses the cubic function at point A(-1,0). Suppose that the straight line crosses the cubic function at two further points P(x_1,y_1) and Q(x_2,y_2), where x_1<x_2. 1. Show that...
  15. A

    MAth Cubics

    what is the cubic eqaution for the follwing coordinates and how do i deduce it? (1,10),(2,23)(3,38)(4,55)(5,74)(6,96)(7,120)(8,149)
  16. P

    Cubics and group law

    (1) Let C:(y^2: = x^3+ 4x), with the simplified group law (2.13) Show that the tangent line to C at P = (2,4) passes through (0,0), and deduce that P is a point of order 4 in the group law. (2) Let C: (y^2=x^3+ax+b)\in \mathbb{R}^2 be nonsingular; find all points of order 2 in the group law...
  17. S


    (2.1) Examples of parametrised cubics. Some plane cubic curves can be parametrised, just as the conics: Nodal cubic C: (y^2=x^3+x^2) \subset \mathbb{R}^2 is the image of the map \varphi: \mathbb{R}^1 \to \mathbb{R}^2 given by t\mapsto (t^2-1, t^3-t) Cuspidal cubic. C: (y^2 = x^3)\subset...
  18. D

    Further maths. Cubics. What?

    Ok this 1 confused my maths teacher! You might need a pen and paper for this.... We have the equation 3x^3 + 6x^2 - 4x +7 = 0 with roots a,b,c we gotta find the equation with root b+c, c+a, a+b We did quite a lot of it this is how far we got... written in the form x^3 - (sum)x^2 + (pairs)x -...
  19. Jones

    Factorizing cubics

    Hi, Is there some kind of formula for factorizing cubic s? By formula i mean. If we have a second degree polynomial x^2+6x+12 we know we need two numbers that multiply to give us 12 and add together to give us 6. Is there any similar forumula for cubics? Im having some difficulties...
  20. D

    Cubics equations

    The equation x^3 + 5x - 10 has only one solution. This solution lies between either a) -2 and -1 b) -1 and 0 c) 0 and 1 d) 1 and 2 e) 2 and 8 The polynomial P(x)= x^4 +ax^2 - 4 has zeros at x = 1 and x = -3. The values of a and b are a) 0 b) 2 c) -2 d) -3 e) 3 Thanks in advance!!(Rofl)