Quadratic Definition and 965 Threads

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...

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...

Homework Statement is an expression that is a difference of two squares considered to be a quadratic. For example, would x2 - 4 be a quadratic? What about x4 - 4? Homework Equations Ax2 + Bx + C The Attempt at a Solution I know we can factor a DOTS into two binomials like a...

Homework Statement If the equations ax2+bx+c=0 and x3+3x2+3x+2=0 have two common solutions then show a=b=c. Homework Equations The Attempt at a Solution first equation will be the factor of second. taking out common from first equation. how to show a=b=c?? please provide...

Homework Statement If 3x2+2αxy+2y2+2ax-4y+1 can be resolved into two linear factors, prove that α is the root of the equation x2+ 4ax+2a2+6=0. please don't solve the problem just hint is expected.

Homework Statement There are 2 beakers P and Q. P contains 50 litres of water and Q contains 40 litres of acid. x litres is taken from both the beakers, mixed and replaced. This process is repeated 2 times and after the second time, there is 71/8 litres of acid in P. What is the quantity of...

Homework Statement (A) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root. (B) Choose a value for K so the equation has no real roots, Use the quadratic formula to prove that this equation has no real roots for your...

Homework Statement f(x)=6x^2+9x-6 Where does this function intersect the x-axis (i.e. what are the roots or zeroes of f(x))? Solve by factoring using the Box Method. When I use the method that is shown on this website http://www.purplemath.com/modules/factquad2.htm for this...

Hi, All: Given a quadratic form Q(x,y) over a field of characteristic different from 2, we can find the bilinear form B(x,y) associated with Q by using the formula: (0.5)[Q(x+y)-Q(x)-Q(y)]=B(x,y). I know there is a whole theory about what happens when we work over fields...

Homework Statement Hello, after searching the internet I found this very active community and hope you can help me with my problem. On the Khan Academy website (Which I highly recommend) there are exercises such as Kinematic Equations. I was asked to solve Vi (Initial velocity) so I used the...

Given: H_0 = x^2 + y^2 + 2axy How does one go about finding the bounds on x and y, based on a? The author of a book I'm reading says that bounds are simple to show based on the different conditions |a|<1, |a|>1, or |a|=1. Unfortunately, I'm not finding it so simple, except for the |a|=1...

Homework Statement Given f(x) = x^2 Sketch the graph of each of the following, state the domain and range. - 1/2f(2x+6) -2 Homework Equations y=x^2 The Attempt at a Solution I Simply have a question. The question is, that this 2x can be factored out from the brackets...