Cubic Definition and 430 Threads

Hello, Homework Statement I get this question from Mathematical Methods by Boas page 74 problem 25. The question states: "Use a computer to find the three solutions of the equation ##x^3-3x-1=0##. Find a way to show that the solutions can be written as ##2cos(\frac{\pi}{9})##...

1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...

Homework Statement Find the real solutions of x^3+6x^2-8x+1 Homework Equations quadraticThe Attempt at a Solution First I tried simple numbers starting with 1 and found that +1 was a solution and therefore I could write x^3+6x^2-8x+1=(x-1)(Ax^2+Bx+C) \\ x^3+6x^2-8x+1=Ax^3+Bx^2+Cx-Ax^2-Bx-C...

1. Homework Statement A permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume s << r. a) Use the binomial approximation (1+x)-n ~= 1-nx if x << 1 to show that the net force exerted...

Homework Statement Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0 Homework Equations I figured it out but I am not sure why we use the equation f(x) = a[x-(-1)](x-0)(x-2) The Attempt at a Solution Im assuming its because if u times that equation that is a...

Homework Statement Find the inverse of f(x)=ln(x^3-3x^2+3x-1) Homework Equations n/a The Attempt at a Solution y=ln(x^3-3x^2+3x-1) x=ln(y^3-y^2+3y-1) e^x=(y^3-y^2+3y-1) i looked around for inverse of cubic functions and i found a monster of a formula...

Can anyone help solve S3+101S2+(10K+100)S+100K to find the roots of S in terms of K

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 5) Express .00024 in Sci Notation My answer: 2.4 x 10^-4 6) Factor the following completely: 3x^3 - 18x^2 + 24x My Answer: (3x)(x - 4)(x - 2)

Homework Statement Factorise: f(x)=x^3-10x^2+17x+28

Prove the following \int^1_0 \frac{\log^3(1-x)}{x}\, dx=-\frac{\pi^4}{15}

The real numbers x and y satisfy x^3-3x^2+5x-17=0 and y^3-3y^2+5y+11=0. Determine the value of x+y.

Find the constants a,\;b, \;c,\; d such that 4x^3-3x+\frac{\sqrt{3}}{2}=a(x-b)(x-c)(x-d).

Homework Statement A table is given: x | -2 | -1 | 0 | 1 | 2 | 3 h(x) | 0 | 9 | y | 3 | 0 | 6 Well actually the h(x) line was based on a graph that we had to look at, it should be right. I discovered y = 8 (the graph increments by 3 on y-axis and 1 on x axis, so I couldn't tell...

Homework Statement When possible express the general solution in explicit form. Solve dy/dx =x^2 /(1+y^2) Homework Equations This is a first order non-linear ordinary differential equation. The Attempt at a Solution dy(1+y^2) = x^2 dx Integration both sides returns: y+ (y^3 )/3=...

Homework Statement Hey I have a question that I have to do that involves expanding a cubic. It is given in the form y = , once it is found I have to square it and then substitute it into a formula to find the area. All I need help with is the expansion than after that it's quite easy.Homework...

Homework Statement 1. a 100m long copper wire of diameter 4mm is heater from 20C to 80C. What is the change in the length of the wire? 2. a 0.2m diameter aluminium sphere is cooled from 250C to 0C. What is the change in the volume of the sphere? The coefficients of linear and cubic expansion...

Homework Statement x3-13x+12=0 The book shows the following solutions, i should add that i have very little practice with factoring cubic TRINOMIALS, you see i factor trinomials through an intuitive understanding, i tried staring at the problem a few hours yesterday, tried youtube/google for...

Hi, If we have this equation: m^3 - m^2 - 8m + 12 = 0 how we can get the roots m_1,\,m_2,\,m_3? can someone please help... ?

Found this on a test for an integrated algebra 2 high school math class! Factor completely. 6x3 - 3x2 + 12 The Attempt at a Solution 3( 2x3 - x2 + 4) eq.1 At this point I checked for rational roots using the rational roots theorem and synthetically dividing. I got nothing...

Here is the question: Here is a link to the question: Math help: factoring? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Dear Everyone, I need some help for this general cubic equation. \[ax^3+bx^2+cx+d=0\]. First divide the equation by a \[x^3+b/ax^2+c/ax+d/a=0\] Let x=y-b/(3a) ... $$y^3+py+q=0$$ where $$p=c/a-(b/a)^2)/3;q=d/a-(b/a*c/a)/3+(b/a)^3/27$$ $$y=cos \theta$$ then i need to use the identity for...

Homework Statement Give an example of a cubic polynomial, defined on the open interval (-1,4), which reaches both its maximum and minimum values. Homework Equations - The Attempt at a Solution I can see that I would need a function such that there is some f(a) and f(b) in...

1. Show that applying a second-order weighted moving average to a cubic polynomial will not change anything. X_t = a_0 + a_1t + a_2t^2 + a_3t^3 is our polynomial Second-order weighted moving average: \sum_{i=-L}^{i=L} B_iX_{t+i} where B_i=(1-i^2I_2/I_4)/(2L+1-I_2^{2}/I_4) where...

Here is the question: Here is a link to the question: Curve Tangent Question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Dear all, I'm trying to understand the second figure of the following webpage. The webpage simply solve it by 'symmetry', but I could not figure out its reasoning. Could someone explain how does it work? Thanks in advance...

Homework Statement I have a line of a cubic function that passes through (-10,4), (-2,3), (-1,2), (0,1), (7,0). I must find the function of this line. Homework Equations The Attempt at a Solution I know you can't see this but the line has a "S" curve to it. Making me assume that...

I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.

Alright, I'm back with yet another question... So the prof was explaining that the energy in an infinite cubical well is E((h2∏2)/2ma2))(nx2+ny2+nz2) Which is all well and good, and he gave us the example of: ψ1,2,1 = E = 6((h2∏2)/2ma2)) And with little explanation mixed it up once...

Homework Statement Find the equation who roots are the squares of the roots of the equation x^3-4x^2+x- is the answer x^3-16y^2+y+1?

Homework Statement A potential electrostatic difference is stablished between points M and Q in the cubic circuit of identical capacitors shown in the image. What is the potential difference between points N and P? Homework Equations The Attempt at a Solution I tried opening up...

My book mentioned that SC and SH are both "Theoretical arrangement" for crystal lattices, and later posed the question "Why it doesn't happen?", however it never provided an answer. Well, I can 'sort of' (very non-scientifically, mind you) imagine why, three stacked layers of spheres(atoms)...

I’ve been scratching my head (and working in ms excel) about the following for about 6 hours and would greatly appreciate it if somebody could help me. Basically, I am trying to figure out WHY the density of water is approximately one gram per cubic centimeter (at 1 atm pressure and 4 degrees...

If a cubic function satisfies f(0) = -32, f(1) = 0, f(3) = 10 and f(4) = 0, use cubic interpolation to estimate f(2) I'm not sure how to approach this since I have only ever done quadratic interpolation and linear interpolation, is it just an extension of the lagrange interpolating...

Here is the correct answer: 2x^3 - x^2 + 4x - 5 My attempt only gives me one cubed term and the other terms are also marginally off, any help on who can show me how to get the correct answer will be hugely appreciated

Such as f(x)=(x^2+1)(x+1)?

Homework Statement A bird dove under water and re-emerged with a fish. Following is the table which shows the bird's estimated flight: Time(s),Height(m) 0, 7 2, 10 4, 5 6, 0 7, 0 8, 3 Find a cubic equation to model the data. 2. The...

is there any general formula to find out zeros of a cubic polynomial that will give you all the zeros ? if not please tell me what are the different methods to find out the zeros , guessing and trial and error , numerical etc. i want to see where are each methods useful and is there...

find a, b, c, and d, such the cubic $f(x)=ax^3+bx^2+cx+d$ satisfies the given conditions Relative maximum (3,3) Relative minimum (5,1) Inflection point (4,2) I approached this by using the f'(x)= a(3)(x^2)+b(2)(x)+c with the min and max and f''(x)=6x+2b for inflection pt to get $27a +6b + c...

I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.

Homework Statement Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming Homework Equations The equation and attempt is shown in the image below, tell me if its unclear :shy: The Attempt at a Solution...

As we know, a quadratic function can be expressed in a form of complete square by a method of completing the square. This form enables us to prove that a quadratic equation is symmetric about its stationary point. But for the cubic function, is there a similar way to prove that the cubic curve...

Homework Statement x^3-8x+10=0 Homework Equations The Attempt at a Solution By dividing by x-1 (1 is a factor of the solution), I got (x-1)(x2+x-7)+3+10=0 which equals x^3-8x+20=0 I think the solution would be imaginary but I used a graphing calculator and there is one...

Homework Statement Graph this equation: P=-0.2t^3+2t^2+8t+2 t belongs to [0,13] Homework Equations The Attempt at a Solution Can't seem to get factored to find x-int. and the rest of the graph.

Homework Statement Given a cylinder of radius = 5m, and height = 10m, how many cubic meters is that? If I just compute those values in the formula for a cylinder, I get 785.4. But 785.4 what? Is it785.4m^3? Homework Equations The Attempt at a Solution

Homework Statement Homework Equations The Attempt at a Solution for 24. which is a quadratic function, i understand that you have to exchange the positions of x and y and solve from there...but my question is the inverse function of that quadratic for 24 is a negative number...

Homework Statement Earth’s radius is 6370 km and approximately 70% of its surface is covered with water, to an average depth of 12,000 feet. Calculate the approximate volume, in km 3 , m 3 , cubic miles and gallons of Earth’s oceans. Homework Equations The Attempt at a...

Alright, so I need a little brush up on my pre calc apparently! I need to determine the x-intercepts of the following function. y=x^3 + 2 I know I need to factor it... I'm just not completely sure how! Thanks!

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...

Why does the standard model have a higgs boson quadratic and a cuartic term but it does not have a cubic term? is there any problem if it happens to have a cubic term? Thanks!

Homework Statement If a cubic equation, f(x) has a factor of (3+√2), then the conjugate of the factor, (3-√2) is also a factor for f(x). Homework Equations The Attempt at a Solution Just to confirm is that statement correct? I read it else where but i not sure is it correct or...