Cubic Definition and 430 Threads

How does one find the roots of an equation, for instance: r^4 + r^3 - 7r^2 - r + 6 = 0 ...completely by hand. Is there some type of non-lengthy process or trick to find special circumstances for easy solving? Thanks.

A 3rd degree polynomial is called a cubic, and a 2nd degree is a quadratic. But quad implies 4. Why is a 2nd degree called quadratic?

Construct a free cubic spline to approximate f(x) = e^ -x , by using values for x = 0 , 0.25, 0.75, 1 now i know i have to contstruct something like this ss_{j} = a_{j} + b_{j} (x - x_{j}) + c_{j} (x-x_{j})^2 + d_{j} (x- x_{j})^3 also we know from the initial conditions that a0 = f(0), but...

With my buddies TI-83 I've plotted a cubic function but am wondering how I can find the x value for a given y value.

Hai, I have a question solving a cubic equation. I have a function y=ax*x*x+bx*x. I want to get a solution for the value of a and b. From reference, I found that a=(xtan(Theta)-2y)/(x*x*x) and b=(3y-xtan(Theta))/(x*x) [Theta] is an angle or tangent of each point x along a cubic curve or...

The determinate of the following 3x3 matrix 1-y, 2 , 3 2 , 4-y, 5 3 , 5 , 7-y gives a cubic that simplifies to, y^3 - 12*y^2 + y + 1 = 0. Now, apparently the teacher picked random numbers for the original matrix, making the problem delve into other realms of mathematics...

volume of a cone is 10 cubic cm... Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper. Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3. I think you solve this...

Just when I thought I understood the concept of planes and miller indices, I got stuck on a 'test your understanding' Q in my book. I can't understand that there can be two or more (110) planes in a crystal lattice? I thought there can be only one such plane. The question asks me to find the...

Hi, all, I'm studying the superconducting qubit based on current-biased josephson junction. The system can be considered as a particle in a washboard well, or a cubic well. The two states |0> and |1> are the ground and the first excited ones. But How to quantize the cubic well. Could anyone...

Maths urgent help If there is a cubic log with a mass "M" and edges which have a length "2a" and is kept on top of a table,and there is a hole dug inside it right in between two parraral faces of this cube. This hole starts from the middle of one top edge(A) and leads on to the bottom of the...

On mathworld's discussion of the cubic formula he has that "determining which roots are real and which are complex can be accomplished by noting that if the polynomial discriminant D > 0, one root is real and two are complex conjugates; if D = 0, all roots are real and at least two are...

Hi, A cubic equation has at least one real root. If it has more than one why are there always an odd number of real roots? Why not an even number of real roots? Can someone help me to prove this? Thx! LMA

Hi, A cubic equation has at least one real root. Can someone help me to prove this? Thx! LMA

Hello, I tried to consider one-dimensional anharmonic (cubic) oscillator in second quantization formalism. And I found that energy difference between the first excited state and the ground state (as well as energy difference between the second excited stated and the the first one) as...

1. Find the equation of a cubic relationship given that the graph has only two x intercepts, one at point (3,0) and the other at (-1,0). It is also known that the graph passes through the point (4,-10) and has a y-intercept of (0,-18) 2. Write down the exact co-ordinates of the two turning...

This is a numerical analysis question, and I am trying to prove that the p(0), p'(0), p(1), p'(1) define a unique cubic polynomial, p. More precisely, given four real numbers, p00, p01, p10, p11, there is one and only one polynomial, p, of degree at most 3 such that p(0) = p00, p'(0) = p01...

It's very easy to solve the equation for x: ax^2 + bx + c = 0 The law for the answer will be (-b+-sqrt(delta))/2a OK, what if i want to solve: ax^3 + bx^2 + cx + d = 0 ax^4 + bx^3 + cx^2 + dx + e = 0 a,b,c,d,e constants, How I'm going to solve this for x? isn't there a general law?

I've been kicking myself trying to think of a few real world applications of cubic equations (and x^4 quintive?). Can anyone give me a few examples? Thanks, Jeremy

Benzun started a thread with this question: I have replied to that question, and want to extend the question (without diverting Benzun's original thead). the related question is, if you have a hollow box or cavity at some temperature T, then how many photons per cubic meter are in it...

hi, just out of curiosity. What is the maximum number of photons that can be accommodated in 1 cubic meter? -benzun

Is there a way (algebraic or otherwise) to find the inverse function of a cubic polynomial? For example: y(x) = x³+x-9 y-1(x) = ?

HELP PLZ! Motion in inverse cubic force field...thx 1000000 in advance! Say a particle expereinces a net force F = -Amr^-3, where A is some constant, m is the mass of the particle (point mass), and r is the distance. How should I go about in describing the possible orbits of the particle with...

How many are there in a cubic in inch?

Is anybody interested in this problem? Solve This One: Victor Niederhoffer in "Education of a Speculator," recalls that he wanted to join his Brooklyn High School Math Team, and prepair for a hope-for entrance to Harvard University, which he achieved. He mentions that he was asked to solve in...

1. Acetone has normal boiling point of 56.5 oC, and heat of vaporization of 32.0 kJ/mol. Find the boiling point at 580 mmHg. 2. Given element, its structure and density, find its atomic radius in pm. Cr, body centered cubic, 7.19 g/mL. Well, as for question 1, I'm totally stumped...

Do I need to use "cc" to represent "cubic centimeters?"

Instead of long ass "formulas" for Cubic and Quartics equations, can someone give some solving techniques? Perhaps in the end attach the formula just in case your hand gets itchy?

For all of those curious mathematicians out there, this one is for you. Click the link below to be redirected to a page with the cubic formula on it. I'm sure that this equation will provide you with a challenge! (If you get the equation solve 4x^3+2x^2+5x-2) Cubic Formula

on a ti83 calculator, how do you put in cubic roots?

One calorie per cubic mile is almost exactly the same as one joule per cubic kilometer. Because a calorie is 4.185 joules and a cubic mile is 4.166 cubic km. And the density of the universe has finally been measured to the general satisfaction of astronomers, at 0.85 joule per cubic...