Polynomial Definition and 1000 Threads

Is there a formula for finding the roots of a bivariate polynomial in x and y with the form: (a^2)xy+abx+acy+bc Where a, b, and c are constants, of course.

hey i'm trying to figure out how to approach part b of this problem, http://imageshack.us/a/img850/6059/asdasdno.jpg so i can see that you can apply the mean value theorem to p'(x) so there exists some c between a and b such that f'(c) = [f(b) - f(a)] / (b-a)=0 so p'(x)...

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...

Question: 1.Find the range of values of \(a\) for which \[(2-3a)x^2+(4-a)x+2=0\]has real roots.2. If the roots of the equation \(4x^3+7x^2-5x-1=0\) are \(\alpha\) , \(\beta\) and \( \gamma\),find the equation whose roots are: (a) \( \alpha+1,\beta+1\) and \(\gamma+1\) (b) \(\alpha^2 \beta^2\)...

Find a polynomial p(t) of degree 6 which has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, and also satisfying: p(0) = 2 and p`(0) = 1. What is the other root of p(t)? Attempt at solution: zero of multiplicity 2 at t =1 implies (t-1)^2 is a factor or p(1) = 0...

Homework Statement Let's say that we have a second order polynomial function, and we know all of the points where it intersects with the x and y axis. Ex: (-2; 0), (0; 2), (1; 0) How does on determine the ax^2+bx+c polynomial form based on that? Homework Equations - The Attempt at...

Homework Statement The problems states "All polynomials of the form p(t)= at^2, where a is in R." I'm supposed to see if it is a subspace of Pn. I've already done that but the book's answer is that it spans Pn by Theorem 1, because the set is span{t^2} Homework Equations Theorem states "1 If...

Homework Statement Let f(x) = x^{4}+ax^{3}+bx^{2}+cx+d be a polynomial with real coefficients and real zeroes. If |f(i)| = 1, (where i = \sqrt{-1}) then find a+b+c+d. Homework Equations The Attempt at a Solution f(i) = 1-b+d+ci-ai Taking modulus |f(i)|= |1-b+d+i(c-a)|...

Homework Statement If we have a transformation matrix \begin{bmatrix} 1 & 2 & 4 \\0 & 0 & 0 \\0 & 0 & 0 \end{bmatrix} Homework Equations The Attempt at a Solution I found the characteristic polynomial of this matrix: x^3 - x^2 = x^2(x-1) ...can anybody please help me...

Homework Statement find the polynomial function p(x) with zeros, -1, 1, 3 and P(0)=9 Homework Equations all i have is (x^2-1) and (x-3) The Attempt at a Solution

Homework Statement if 2 is a root of 4x^3-3x^2-kx-4k^2= 0 find th value of k Homework Equations The Attempt at a Solution

The first thing that we should notice is that the leading coefficient $a_n = 1$. I was thinking about considering the factored form of p. I googled, and there is an algorithm called the "Schur-Cohn Algorithm" that is suppose to answer exactly this, but I can't find any information on it or...

Homework Statement Consider the vector space F(R) = {f | f : R → R}, with the standard operations. Recall that the zero of F(R) is the function that has the value 0 for all x ∈ R: Let U = {f ∈ F(R) | f(1) = f(−1)} be the subspace of functions which have the same value at x = −1 and x = 1...

Homework Statement Consider the vector space F(R) = {f | f : R → R}, with the standard operations. Recall that the zero of F(R) is the function that has the value 0 for all x ∈ R: Let U = {f ∈ F(R) | f(1) = f(−1)} be the subspace of functions which have the same value at x = −1 and x = 1...

Taking the derivative of a polynomial fraction?? b]1. Homework Statement [/b] Ok, so the question wants me to differentiate f(x)= (x)/(x+1). We are supposed to use the definition of the derivative f'(x)= (limit as h->0) [f(x+h)-f(x)]/(h). We also have learned the power rule. I did the formula...

Could someone quickly go over my working, as I am not 100% sure I have done it the right way. I will show and explain my working step by step. $$ at^2-4a + 2t^2-8$$ I first grouped the values: (at^2-4a) + (2t^2-8) I then factorised these equations into: a(t^2-4a) + 2(t^2-4) I...

Hello, This was an exam question which I wasn't sure how to solve: Suppose f is entire and |f(z)| \leq C(1+ |z|)^n for all z \in \mathbb{C} and for some n \in \mathbb{N}. Prove that f is a polynomial of degree less than or equal to n. I know that f can be expressed as a power series, but I'm...

Suppose there is a set of complex variables \{x_i,\,i=1 \ldots M;\;\;y_k,\,k=1 \ldots N\} and a polynomial equation p(x_i, y_k) = 0 Is there a way to prove or disprove for such an equation whether it can be reformulated as f(x_i) = g(y_k) with two functions f and g with...

Homework Statement Determine whether the following are subspaces of P4: a) The set of polynomials in P4 of even degree b) The set of all polynomials of degree 3 c) The set of all polynomials p(x) in P4 such that p(0) = 0 d) The set of all polynomials in P4 having at least one real root The...

Let [ tex ]f(x)=\sum_{i=0}^n c_i x^i[ / tex ] be an arbitrary polynomial function of degree n Show that if f(0)=0 then either f is constant or f(x)=xg(x), where g is a polynomial function of degree n-1 I don't know how to start. Please help Thank you in advance

Dear All Friends, I am currently working on a project which needs some orthogonality integration formulae of Laguerre polynomials. I referred worlfram's math function site http://functions.wolfram.com/Polynomials/LaguerreL3/21/02/01/ and get three seemingly useful ones...

Homework Statement let A be a UFD and K its field of fractions. and f\in A[x] where f(x)=x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0} is a monic polynomial. Prove that if f has a root \alpha=\frac{c}{d}\in K,K=Frac(A) then in fact \alpha\in A I need some guidance with the proof. Proof...

Homework Statement Let p be a polynomial. Show that the roots of p' are real if the roots of p are real. Homework Equations The Attempt at a Solution So we start with a root of p', call it r. We want to show that r is real. Judging by the condition given, I am assuming that...

Homework Statement Give an example of a polynomial irreducible in Q[x], but reducible in Z[x] Homework Equations The Attempt at a Solution I think there is no example of this. The coefficients of a reducible polynomial with integer coefficients will be rational, or am I mistaken?

Homework Statement Show that for any square matrices of the same size, A, B, that AB and BA have the same characteristic polynomial. Homework Equations The Attempt at a Solution I understand how to do this if either A or B is invertible, since they would be similar then. I saw a...

I have a small idea on what irreducible and primitive polynomials are in Abstract algebra. But what is minimal polynomial? -Devanand T

Homework Statement Hi An integration question: t= 1/(1+r2) Can you please show me how to integrate with respect to r. Thank you. The Attempt at a Solution ∴t = (1+r2)-1 I then tried substituting u = 1+r^2 but that didn't work! Is there a trick with this?

I have a quick question. The problem reads: Prove that there is no integer m such that 3x2+4x + m is a factor of 6x4+50 in Z[x]. Now, Z[x] is not a field. So, the division algorithm for polynomials does not guarantee us a quotient and remainder. When I tried dividing 6x4+50 by 3x2+4x +...

Homework Statement Applying remainder theorem again and again to show that the remainder of the f(x) polynomial function when divided by (x-α)(x-β) is A(x-α)+B . Determine A and B Homework Equations the remainder of a polynomial f(x), divided by a linear divisor x-a, is equal to f(a) The...

Can I use excel to make an equation for 4 variables (x,y,z,w) e.g a,b,c,d,3,f,g,h,i, would be constants w = ax + by + cz + dx^2 + ey^2 + fz^2 + gxy + hyz + iyz What are these equations called ? What literature can I study to better understand the procedure of making these tye of...

i need the derivation of orthogonal properties of associated laguerre polynomial (with intermediate steps). someone please tell me where can i get it (for easy understanding).

I understand that mathematicians have had to define the number '0' also as a polynomial because it acts as the additive identity for the additive group of poly's.What I do not understand is why they define the degree of the zero polynomial as [ tex ]-\infty[ /tex ]. An explanation on planetMath...

Background information: I have come up against a mathematical question which I as somebody with relatively limited exposure to maths can not seem to answer. I am a student working on a thesis dealing with near-infrared spectroscopy (NIRS). The NIR scanner is able to measure the moisture content...

Let's say I have the equation f(x) = 2x + 3 * (3x^2 + 3) - x^2 + 5. If my algebra is right, this is a 3rd-degree polynomial. How many zeroes does this equation have? How did you figure that out?

Homework Statement My teacher likes to teach us the D-notation methods for higher order DE's. I am having a hard time with this one and I can't seem to find the formula for the general solution Find a fundamental set of the equation (D-1)^{2}(D^{2}-6D+13)^{3}y = 0 Homework...

Homework Statement What are the steps to factoring 3rd order polynomials like x^3+8x^2-21x+10? It's to find eigenvalues of a matrix in linear algebra, I completely forgot how to factor and it's killing me. Homework Equations The Attempt at a Solution None, unless its a polynomial...

I couldn't get these lines from my book. I will reproduce it here. Warning: In step 1, if you use computer to fit a polynomial to the data , it could lead to disaster. For example, consider fitting a sixth degree polynomial to the seven data points, or, an (n-1) degree polynomial to n...

factor completely 2x3 - 8a2x + 24x2 + 72x so far i got 2x(x2 + 12x + 36) - 8a2x 2x(x+6)(x+6) - 8a2x don't know what to do from here.

Unless I'm missing something here, I've noticed that if you want to store a polynomial function on the TI-83 or the TI-84 Plus, you have to create a program that asks you what the value of x is, then displays the value of f(x). I kind of wish I could define a function without making a program.

I'd like to know how to find the root of a polynomial on my TI-84 Plus without this "Polynomial Root Finder and Simultaneous Equation Solver" app. The reason is that the app's not in my calculator and I can't transfer the app to my calculator. I keep getting an "Access Denied" error message...

The problem is :- Integral of (1+x^4) / ( 1 + x^6) . dx I have reduced it to a form of Integral of 2.sqrt(tantheta) / ( 1 + tan^3 theta ) over dtheta where x^2 = tantheta. However I cannot reduce it further. How do I proceed ? In general, how do I proceed given a problem of the form...

Are the roots of a polynomial given by the function f(x) defined as the values for x where f(x)=0? Does that mean f(x)=x^2 has only one root? Even though for every other value of x except zero there are two values for x that you can input to output a particular value for f(x). What about...

Homework Statement (A somewhat similar question to my last one). Let J be the ideal of the polynomial ring \mathbb{Q}[x] generated by x^2 + x + 3. Find the multiplicative inverse of (3x^3 + 3x^2 + 2x -1) + J in \mathbb{Q}[x]/JHomework Equations The Attempt at a Solution I think I need to apply...

Homework Statement Factorize x^2 + x + 8 in \mathbb{Z}_{10}[x] in two different waysHomework Equations The Attempt at a Solution I can see that x = 8 = -2 and x = 1 = -9 are roots of the polynomial, so one factorization is (x + 2)(x + 9). Is there a systematic way to find all the factorizations?

Suppose you look at polynomials, P(x), of degree n, with all nonzero integer coefficients and, in particular, a coefficient of 1 for the nth degree (leading) term. And look at those polynomials whose squares have the fewest number of nonzero integer coefficients possible. Examples...

Find an approximate value of the number e-0.1 with an error less than 10-3 ı know that ex = Ʃ(from zero to ınfinity) xn / n!=1+x/1!+x 2/2!+... ı don't know how to use e-0.1 in this question.Do ı write -0.1 instead of x in ex series?

Homework Statement If α, β and γ are roots of cubic polynomial and: αβγ = 6 α2+β2+γ2=20 α3+β3+γ3=121 Find the equation of cubic polynomial Homework Equations vieta The Attempt at a Solution The equation is in the form: x3 - (α+β+γ)x2 + (αβ + αγ + βγ) x - αβγ = 0 But I...

Now if I have a function y=(ab+ac)/a, it can be further factorised, y=(a(b+c))/a. Now if we cancel off the a, we will have only y=b+c that will also give the same y-values as the original form of the function y with respect to the same x-value. This statement implies that cancellation or...

Homework Statement For any quadratic polynomial ax2+bx+c having zeros β and α Prove that β + α = -b/a and αβ = c/a. Homework Equations The Attempt at a Solution I have found a method myself to prove α+ β = -b/a. However, I could not prove αβ = c/a. It goes like this. If α and β are the...

Is there a way to convert a rational bezier curve to a piecewise series of one or more polynomial bezier curves with minimal loss in accuracy, specially cubic ones? I've already tried searching the internet for pre-existing algorithms, but I haven't been able to find any usable results despite...