# coefficients

1. ### Calculating Variances and Regression Coefficients

This first part I am just looking for confirmation that I am working it correctly: I have 30 observations and sumX=30, sumX2=150, sumY=120, sumY2=1830 and sumXY=480. I found the variance of X to be V[X]= E[X2] - (E[X])2= (150/30) - (12) = 5 - 1 = 4 the variance of X to be V[Y]= E[Y2] - (E[Y])2=...
2. ### Problem With Binomial Coefficients

Hello, I am trying to solve the following problem: "Find the term independent of x in (x+\frac{1}{x})^3)^8 ." I think this formula applies, but I am not sure where to begin: t_{k+1}={n \choose k}x^{n-k}y^k. Can anyone help with this question?
3. ### Binomial Theorem with coefficients

I can get the binomial theorem to work just fine when doing (a+b)^n but it becomes a problem as soon as I put coefficients, e.g.: (2a+3b)^n Why? What is the difference and how do I calculate with coefficients?
4. ### Cubic polynomial - complex coefficients HELP ME PLEASE

Hello people! Help would be greatly appreciated... z3 + (1 - 4i)z2 + (17 - 16i)z + (-87 - 116i) = 0, where z = 3 + 4i is one of the roots... step by step working would be fandabadosy too; I know it's pretty basic but I've gone COMPLETELY blank Cheers!
5. ### How changes on coefficients affect the solution of the system

Hi, Let the linear system Ax=b. I am looking for literature describing how changes on coefficients matrix A affect the solution of the system x. For example if the value of the (i,j) element is doubled how this will affect the solution x? Are there standard techniques applying to any linear...
6. ### Least squares to matrix to poly coefficients

I am writing programming code to develop a polynomial equation from x,y data. I am using the least squares procedure to develop various sums to fill a matrix. Once the matrix is filled, computing poly coefficients is straight forward matrix algebra. I have 29 reps of data that look like: Rep...
7. ### General question about comparing coefficients

Hi I know that if ax^2 + bx + c = dx^2 + ex + f then a=d, b=e and c=f but how do we know this? Of course it seems intuative but does it need to be proved? Thanks!
8. ### Finding the constant coefficients in a simple linear model

Let X~exp(1), Y=e-X and consider the simple linear model Y= \alpha + \beta X + \gamma X^2 + W with E(W) = 0 = \rho(X, W) = \rho(X^2, W) I need to evaluate the constants alpha, beta, and gamma using the information given above. I'm wondering if I am doing this correctly. I showed that...
9. ### Help in analysing the coefficients

Can someone help me to analyse these coefficients Saleprice = -62936.05+ -28152.85Bedrooms(i)+ -1729.382HalfBaths(i)+ 29036.28FullBaths(i)+ 133.2546LivingArea(i)+ 19080.43Condition(i)+339.6787PctCollege(i)+ 2.108055Age(i)+ 2196.120LotSize(i)+8098.126Fireplace(i)+ ε Do they have the expected...
10. ### Finding the value of unknown coefficients using a known factor

This one is really wrecking my head. I've been working on this for hours and I just can't seem to get the correct answer. I'm starting to think there is an error in the textbook, but I've been studying for hours and I think I may just be losing my focus. The question is: Find the value of p...
11. ### Polynomials with integer coefficients - the GCD identity

I am reading Anderson and Feil on the Factorization of Polynomials - Section 5.3 Polynomials with Integer Coefficients A&F point out that some of the therems they have proved for \mathbb{Q} [x] are false if we restrict ourselves to polynomials with integer coefficients. For example they...
12. ### relating unkown coefficients with a known factor of a polynomial

Hi, I think this is in the right place. I think it's also very simple but the text book I'm working from just doesn't explain it. The question is: If x + p is a factor of ax2 + bx + 3, show that p(b - ap) = 3 According to the book, I think what they want one to do is long division and then...
13. ### Bijective Proof Involving Binomial Coefficients

How can I derive a bijection to show that the following equality holds? 2\displaystyle\sum\limits_{j=0}^{n-1} \binom{n-1+j}{j} = \binom{2n}{n} In class, we've been deriving bijections using lattice paths in-order to order to show that the size of both sets are the same. So for example, in...
14. ### zeros of a polynomial with complex coefficients

How do I find the roots of this polynomial with complex coefficients: p(z) = z2-(1+2i)z + (- (3/2)+2i) Is there a general method?
15. ### Polynomial with real coefficients but complex roots

Hi everyone I'm trying to solve this equation: z4+1 = 0 I've tried every method I can think of, such as De Moivre's formula, but I only get two complex roots. What method do I use ? I just want to know the method/procedure.
16. ### Second order differential equation with non constant coefficients.

Hi all, While solving some physics problem I came across a differential equation. \frac{\mathrm{d}^2y}{\mathrm{d}x^2}+c_1x^2y=c_2y Where all the constants c_1 and c_2 are positive. I need a solution for this equation. Please indicate me how to go about this. It will be helpful if the...

18. ### Sum of coefficients on polynomial

Hello. There's this problem in my algebra book: Problem 101. Imagine that the polynomial (1+2x)^{200} is converted to the standard form (the sum of powers of x with numerical coefficients). What is the sum of all the coefficients? My solution. The solution of this problem is 2^{200} I think, am...
19. ### relationship between coefficients of a quadratic equations

The condition that a root of the equation may be reciprocal to a root of is Possible Answers Possible Answer
20. ### How to "predict" coefficients in quadratic equation?

I am working on a mathematic study for my work and need your advice on quadratic equation. I will use a modified and simplified example to explain the problem I am facing. To put it simply, I now have say 5 quadratic equations (in the form of y=ax2+bx+c) which give five similar but not...