Quadratic Definition and 990 Threads

Homework Statement Get an inverted quadratic equation (-x^2) with maximum y=100 and roots x=0 and x=1/120. Homework Equations The Attempt at a Solution I tried changing the several terms of the quadratic equation, used the quadratic formula setting c=100, and x=0 with the...

I am reading Dummit and Foote Chapter 7. D&F use a quadratic field as an example of a ring. I am trying to get a good understanding of this ring. D&F define a quadratic field as follows: Let D be a rational number that is not a perfect square in and define \mathbb{Q} ( \sqrt D ) =...

Homework Statement Hey guys, recently, I struggled to solve this equation. I need to find θ1 and θ2 by using this system of equations: θ1+θ2=γ θ1*θ2=β After letting θ2=β/θ1, I plugged this into the first equation. I got: θ12-γθ1+β=0 At this point I get a very unsexy θ1 result by using...

Hi, Everyone: I have a job interview tomorrow where I must give a 10-min presentation on the quadratic formula for an intro class , where we are assuming students know both how to factor and how to complete the square. Please comment: Homework Statement O.K. We are given an equation...

Homework Statement How should be the value of a so quadratic equation ax^2-4x+4=0 to have double solutions? A)\;\;2 B)\;\;1 C)\;-1 D)\;-2 Homework Equations The Attempt at a Solution D=b^2-4ac If: D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}...

Homework Statement L-1(1-(Lambda1+Lambda2)L+Lambda1Lambda2L2)Ft Use quadratic formula to solve for Lambda1 and Lambda2 The Attempt at a Solution I took the equation inside the brackets and solved for L. It turned out that L1=Lambda1 and L2=Lambda2 But when I plugged those...

Homework Statement Use the form of the definition of the integral to evaluate the following: lim (n \rightarrow ∞) \sum^{n}_{i=1} x_{i}\cdotln(x_{i}^{2} + 1)Δx on the interval [2, 6] Homework Equations x_{i} = 2 + \frac{4}{n}i Δx = \frac{4}{n} Ʃ^{n}_{i=1}i^{2} =...

Homework Statement Two platforms 50m in height have targets on them. An object succeeds in impacting with both of these. S=ut + ½ at2 can be rearranged into the form: ½ at2 + ut – s =0 This is a quadratic equation. [ ax2 + bx +c =0 ] Use this to calculate: I. The times at which the...

Homework Statement Hi. I've got the matrix from the Quadratic Sieve down to Gaussian Form and I'm wondering how to find the factor base which leads to a square number now. Homework Equations The Factor Base: $${29,782,22678}$$ The original Matrix: \begin{pmatrix} 0 & 0 & 0 & 1\\...

Hello PF! I'm having trouble approaching this problem. Any assistance would be greatly appreciated. Homework Statement A rectangle with area of 35 cm2 is formed by cutting off strips of equal width from a rectangular piece of paper. The rectangular piece of paper is of 7cm width and 9cm...

Homework Statement \alpha and \alpha^{2} are two roots of the equation x^{2} -12x + k = 0 Find 2 values for k. The Attempt at a Solution \alpha + \alpha^{2} = 12 \alpha^{3} = k I have no idea where to go from here. Any help appreciated.

Hi guys, I'm really confused in finding the domain of quadratic equations. For example: when finding a suitable domain so that an inverse exists, why is the domain of x2-4 x>0 whilst, the domain of 2x2+3 is x≥0 Can the domain of x2-4 be x≥0? Furthermore, what is the largest domain and how do...

Homework Statement y^4 + 3y^2 - 4 = 0 Homework Equations The Attempt at a Solution The base, I know, is y^2. So in order to make this a quadratic equation, we come up with an arbitrary variable, say α, which is equal to the base. Re-writing this, we get: (y^2)^2 + 3(y^2) - 4 =...

Say I start with a quadratic form: x^2 - y^2 - 2z^2 + 2xz - 4yz. I complete the square to get: (x+z)^2 - (y+2z)^2 + z^2. (So the rank=3, signature=1) The symmetric matrix representing the quadratic form wrt the standard basis for \mathbb{R}^3 is A =\begin{bmatrix} 1 & 0 & 1 \\...

Homework Statement The graph of the quadratic polynomial , y=ax2+bx+c is as shown below in the figure : http://postimage.org/image/nvkxv74yd/ Then : (A) b2-4ac<0 (B) c<0 (C) a<0 (D) b<0Homework Equations y=ax2+bx+c If y=0 , then ax2+bx+c=0 Then , x = {-b+-sqrt(b^2-4ac)}/2a The Attempt at...

find the irreducible quadratic factors of z^(4)+4 The Attempt at a Solution Im stumped...this is all I've got: [(z^(2))^2]-[(2i)^2] (z^(2)-2i)(z^2+2i) Any guidance is greatly appreciated!

Homework Statement I need to find Vi, knowing the following: Δt=6/Vi cos40 Viy=Vi sin40 Δy=4m ay=-g = -9.8m/s^2Homework Equations Quadratic: x= [-b +/- √(b^2-4ac)]/2a Kinematic equation to be used: Δy=ViyΔt + 1/2ayΔt^2The Attempt at a Solution Δy=ViyΔt + 1/2ayΔt^2 4=(Vi sin40)(6/Vi...

Homework Statement The equation kx2 - 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k. Homework Equations Since the equation has two distinct real roots, b2 - 4ac > 0 The Attempt at a Solution b2-4ac>0 9-4(k+2)(k)>0 9-4(k2+2k) >0 9-4k2-8k>0 =...

Homework Statement Solve using the formula method. Homework Equations 3t^2+7t=5 The Attempt at a Solution 3t^2+7t-5=0 t= \frac{-7 +or-\sqrt{7^2-4(3)(-5)}}{2(3)} t= \frac{-7+\sqrt{109}}{4} t= -4.39 OR... t= \frac{-7-\sqrt{109}}{4} t= -9.61 The reason I have doubts is...

f(x) = –3√x, 1 ≤ x ≤ 4 (a) Find the quadratic least squares approximating function g for the function f. g(x)=?

Homework Statement Find the intervals of all possible value of p which the equation equation: (p-1)x^2+4x+(p-4)=0 has two different roots. Homework Equations ax^2+bx+c>0 ?? The Attempt at a Solution (p-1)x^2+4x+(p-4)>0 ?? How would I go about solving this? Is two roots...

I'm having a bit of a brain fart here. Given a positive definite quadratic form \sum \alpha_{i,j} x_i x_j is it possible to re-write this as \sum k_i x_i^2 + \left( \sum \beta_i x_i \right)^2 with all the ki positive? I feel like the answer should be obvious

Homework Statement Solve each equation for 0≤\Theta≤2\pi (exact values where possible) The question: 2cos^22\Theta - cos2\Theta - 1=0 Homework Equations cos2\Theta = 2cos^2\Theta-1 The Attempt at a Solution 2cos^22\Theta - 2cos^2\Theta - 1 - 1 = 0 2cos^22\Theta - 2cos^2\Theta - 2 = 0...

Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables, ax^{2}+by^{2}+2gx+2fy+2hxy+c=0? Thanks!

Homework Statement Consider the quadratic form q(v) = x12 + 5x22 + 11x32 + 4x1x2 + 6x1x3 + 14x23 Relative to the standard basis of R3 find the symmetric matrix A associated with q. The Attempt at a Solution In the standard basis, I'll use e1 = [1,0,0] e2 = [0,1,0] e3 = [0,0,1] if it were in...

Homework Statement (a) The quadratic Chebyshev approximation of a function on [-1, 1] can be obtained by finding the coefficients of an arbitrary quadratic y = ax^2 + bx + c which fit the function exactly at the points (-sqrt(3)/2), 0, (sqrt(3)/2). Find the quadratic Chebyshev approximation of...

Homework Statement the question asks to find the quadratic maclaurin polynomial for f(x) Given f(x) = x sin(x)The Attempt at a Solution i know that a maclaurin series is when a=0 in a taylor series. i did the 1st-5th derivatives of f(x) and then used the formula for taylor polynomial and set...

Homework Statement given that kλ2-ρcpuλ-ρcpωi=0 plug into the quadratic formula and get out an equation that looks like this λ=α+iβ±γ√(1+iδ) where α,β,γ,and δ are in terms of ρ,cp,u,k, and ω Homework Equations (-b±√b2-4ac)/2a kλ2-ρcpuλ-ρcpωi=0 λ=α+iβ±γ√(1+iδ) The Attempt at a...

Homework Statement Is it true that all quadratic equations (ax2+bx+c) can be factorised into this form: (ax+b)(cx+d)? I think so, but I'm not certain.

\frac{d}{dx}f(x)=\frac{d}{dx}[ \frac{1}{2}x_{}^{T}Qx-b_{}^{T}x] how to get this derivative, what is the answer? is there textbook describe it?

\frac{d}{dx}f(x)=\frac{d}{dx}[ \frac{1}{2}x_{}^{T}Qx-b_{}^{T}x] how to get this derivative, what is the answer? is there textbook describe it?

Homework Statement A particle of mass "m" whose motion start with downard velocity V0 in a constant gravitational field. The drag force is quadratic and proportional to kmv2. What is the distance s through which the particle falls in accelerating from v0 to v1. Give your expression for s in...

Homework Statement Write the following quardatic surface equation as a sum of multiples of squares of independent linear functions x^{2}+4y^{2}+56z^{2}+2xy+4xz+28yz Homework Equations The Attempt at a Solution Please see attachment. nb. there is no answer provided by...

Is the discriminant, of the quadratic equations, the difference between the two roots? Or is it a special case?

Homework Statement The following is a modification of Newton's method: xn+1 = xn - f(xn) / g(xn) where g(xn) = (f(xn + f(xn)) - f(xn)) / f(xn) Homework Equations We are supposed to use the following method: let En = xn + p where p = root → xn = p + En Moreover, f(xn) = f(p + En) = f(p) +...

√(2gH)(M-m)=mV+M√((2gH(M+m)-mV^2)/M) Solve for V in terms of given terms.

I have the PDE: (v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z). I have some boundary conditions, of sorts: p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity p=0 at f=r, where (f_r)^2=p*r/v-v*v_r (f_z)^2=p*r/v+v*v_r Is it possible that one could obtain an...

Homework Statement Hi. I actually understand most of this question, but not the parts in red. Question. http://img703.imageshack.us/img703/7237/2008testhphysf.jpg If above doesn't load, please go to [PLAIN]http://img703.imageshack.us/img703/7237/2008testhphysf.jpg Homework...

Homework Statement okay I know understand that I should get a reasonable understanding about the questions I post before I post them sorry about before. An Illinois farmer will plant from 800 to 2000 acres of soybeans. The number of acres q that he will plant depends on the selling price...

Homework Statement Eastern Ceramics can sell up to 200 of its flower pots per day in accordance with the demand function. p=13 -.04q write revenue as a function of the quantity sold q. find the output level q that maximizes R and the selling price at this output level.Homework Equations The...

Homework Statement Examining the answers of the previous two questions, write the quadratic polynomial f(x1,x2,x3)=x1x2−6x22+3x2x3−3x23 in the form f(x1,x2,x3)=[x1x2x3]A[x1x2x3]<-this last group is a column matrix where A is a symmetric matrix. Homework Equations Matrix multiplication...

I have 2 questions about -b and - 4ac in the formula... x = (-b +-sqrt(b^2 - 4ac))/(2a) If you are given 2nd degree equations at random (that can be solved using above formula) Question1: What percent of the equations given would you expect to compute a double negative for -b? Question2...

Homework Statement What will be the values of 'm' so that the range of the equation y= \frac{mx^2+3x-4}{-4x^2+3x+m} will be all real values i.e. y\epsilon (-\infty,\infty)given:x can take all real values. any help or hint will be appreciated. Homework Equations The Attempt at a Solution i...

Hi, All: I am trying to see how to classify all symmetric bilinear forms B on R^3 as a V.Space over the reals. My idea is to use the standard basis for R^3 , then use the matrix representation M =x^T.M.y . Then, since M is, by assumption, symmetric, we can diagonalize M...

Solve for x-- the inequality of quadratic Homework Statement Solve \frac{2x}{x^2-9}\le\frac{1}{x+2} The Attempt at a Solution x^2-9\not=0 .'. x\in R-\{-3,3\} and x+2\not=0 .'. x\in R-\{-2\} then converting the original inequality to (2x)(x+2)\le(x^2-9)...

Hello, I have a quick question regarding Calculus and what should be covered in pre-cal. I'm currently in a pre-cal course and according to the syllabus it seems the teacher is skipping over quadratic functions. I only noticed because for the most part her course just follows along with the...

Maths Quadratic Question Homework Statement Find the interval in which 'm' lies so that the expression \frac{mx^2+3x-4}{-4x^2+3x+m} can take all real values ,where x is real. The Attempt at a Solution i have equated this equation to y y=\frac{mx^2+3x-4}{-4x^2+3x+m}...

Homework Statement x12+x1x2+2x22=8 a) Write the equation using a quadratic form i.e. \underline{x}TA\underline{X}=8 b)Find the Matrix Q such that the transformation \underline{X}=Q\underline{Y} diagonalises A and reduces the quadratic form to standard form in terms of coordinates...

Homework Statement Find the least integral value of k for which the quadratic polynomial (k-2)x2 + 8x + k+4 > 0 where x is real. The Attempt at a Solution i am trying to solve the discriminant by equating it to>0 D>0 but i don't think it is correct. Please...

Homework Statement if ax2+2bx+c=0 and a1x2+2b1x+c1 have a common root and a/a1 ,b/b1 ,c/c1 are in A.P. show that a1,b1,c1 are in G.P. Homework Equations The Attempt at a Solution I know the mean formula of A.P. i.e. the middle term is the mean of the other two. any hints...