Quadratic Definition and 989 Threads

I am reading "Introductory Algebraic Number Theory"by Saban Alaca and Kenneth S. Williams ... and am currently focused on Chapter 1: Integral Domains ... I need some help with the proof of Theorem 1.2.2 ... Theorem 1.2.2 reads as follows: In the above text from Alaca and Williams, we read the...

Let A and B be the roots of the quadratic equation ax^2 + bx + c = 0. Verify each statement below. 1. A + B = -b/a 2. AB = c/a I need help getting started for parts 1 and 2. I will do the math.

Find the equation of the straight line(s) which pass through the point (1, −2) and is (are) tangent to the parabola with equation y = x2 No calculus is to be used.I can substitute the point into the equation for the straight line giving -2=m+c And into the parabola (-2)2 = m+c Not sure if...

Homework Statement A circus cat has been trained to leap off a 12 m high platform and land on a pillow. The cat leaps off at v_0 = 3.5 m/s at an angle of 25 degrees. Where should the trainer place the pillow so that the cat lands safely? What is the cats velocity as she lands on the pillow...

Homework Statement Algebra - I.M. Gelfand, Problem 164. Prove that a polynomial of degree not exceeding 2 is defined uniquely by three of its values. This means that if P(x) and Q(x) are polynomials of degree not exceeding 2 and P(x1) = Q(x1), P(x2) = Q(x2), P(x3) = Q(x3) for three different...

Homework Statement [/B] Suppose a quadratic equation in 3 variables is put into a standard form represents a hyperboloid of one sheet. This hyperboloid has the property that: • the cross section through z= 0 is a circle of radius 1; • the cross section through x= 1 is the two straight lines...

quadratic equation ||v||^2 - c(2v·w)+c^2||w||^2=0, where c belongs to any real number, v and w are both vectors

Problem: Express the quadratic form: q=x1x2+x1x3+x2x3 in canonical form using Lagrange's Method/Algorithm Attempt: Not really applicable in this case due to the nature of my question The answer is as follows: Using the change of variables: x1=y1+y2 x2=y1-y2 x3=y3 Indeed you get...

##\theta(\tau, A) = \sum\limits_{\vec{x}\in Z^{m}} e^{\pi i A[x] \tau } ## ##=\sum\limits^{\infty}_{n=0} r_{A}(n)q^{n} ##, where ## r_{A} = No. [ \vec{x} \in Z^{m} ; A[\vec{x}] =n]## where ##A[x]= x^t A x ##, is the associated quadratic from to the matrix ##A##, where here ##A## is positive...

Homework Statement Express the quadratic equation ##x^2-6x+20## in the different form hence find,## 1. α+β, αβ , α^2+β^2## Homework EquationsThe Attempt at a Solution ## -(α+β)= -6 ⇒α+β= 6, αβ=20## [/B] now where my problem is finding ##α^2+β^2## , i don't have my reference notes here...

Homework Statement Solve sin2x + sinx =0 Homework EquationsThe Attempt at a Solution I first factor and get sinx(sinx + 1) = 0 sinx = 0 x = sin-1(0) x= 0 x= π-0 = π sinx = -1 x= sin-1(1) x= π/2 x = π + π/2 = 3π/2 x = { 0, π, 3π/2 } However when I look at the solution this is correct but...

Homework Statement How to solve for kd or equation with 2 unknowns given: b= 10 n= 8 As = 2.37 Homework Equations [/B] for the quadratic equation b * (kd)^2 /2 - n * As (d - kd) = 0 The Attempt at a Solution should one use algebra, calculus, what? how do you solve for kd? this is not...

Homework Statement A generalized potential suitable for use in a covariant Lagrangian for a single particle. This is Goldstein problem 9 chapter 7. −Aλν(xμ)uλuν where Aλν stands for a symmetric world tensor of the second rank and u^v are the components of the world velocity. If the...

Homework Statement We had this elementary experiment in class. An aluminium rod is fixed at one end and at the other end you have a disk. You hand increasingly heavy weights on the disk and measure how much the rod shears (twists). We were asked to make a graph of the shear torque vs. angle of...

Homework Statement Reduce ##xy+zy## to diagonal form. Homework Equations The desired diagonal form is ##Q(\vec{x})=(\alpha_1(\vec{x}))^2+...+(\alpha_k(\vec{x}))^2-(\alpha_{k+1}(\vec{x}))^2-...-(\alpha_{k+l}(\vec{x}))^2,## where ##\alpha_i## are linearly independent linear functions. Also known...

$\tiny{206.11.1.12}$ $\textsf{a.Find the linear approximating polynomial for} \\$ $$\displaystyle f(x)=\cos{x} \textsf{ centered at $\displaystyle a=\frac{\pi}{4}$.} \text{approximate} \cos(0.28\pi)$$ $\textsf{ using}$ $$f(x)=f(a)+f'(a)(x-a)$$ $\textsf{b. Find the quadratic approximating...

Hi I am writing my final Mathematics exams for Grade 12 in South Africa in 5 days. I am well prepared with an aim of getting 100%, but one concept in functions might prevent that - the concept of how the nature of roots are affected by vertical/horizontal shifts in a function, and how to...

HI! I'm not sure if this can go in precalculus or not because I'm from Australia, and our Maths subjects don't get that specific until university level. 1. Homework Statement For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of...

$-x^2+4x-1$ should be converted to the vertex form of $y=k-(x-h)^2$ How can this be solved by factoring or any other method ? My attempt to solve this problem , I will be using the completing the square method, $\left(-x^2+4x+\frac{-b}{2a}\right)=1+\frac{-b}{2a}$ Here $\frac{-4}{-2}=2$...

Hey, all! I'm learning partial fraction decomposition from Serge Lang's "A First Course in Calculus." In it, he gives the following example: \int\frac{x+1}{(x-1)^2(x-2)}dx He then decomposes this into the following sum: \frac{x+1}{(x-1)^2(x-2)} =...

Is it possible to factor a quadratic equation along the lines of asin^2x -bsin2x+c ? If so, how? The sin2x seems to be a problem since when expanded it becomes 2sinxcosx, but I'm wondering if it is possible, and how it would be done? Thanks in advance.

Homework Statement X^2-yx+y^2-7=0 Homework Equations -b +- sqrt(b^2-4ac)/2a The Attempt at a Solution Trying to complete the square with two variables (x^2-yx)+(y^2)=7 (X^2-yx+y/2)+y^2=7 Where else from here. I'm just having problems because of the y variable

Write a quadratic function y whose maximum value is 4 and the axis of symmetry of the graph is x=-2. Suggestions?

Homework Statement I'm looking for an explanation to something. I've attached a picture of the solution wolfram alpha is giving me. I understand the first two zeros, +- (-1)^(1/4)*sqrt(2). But i don't understand the other two zeros with the 3/4 power. Where does that power come from...

Hi all I'm trying to work out how to answer this type of problem. (6x+2z)^2-64=(ax+2z+8)(-8+bx+cz) where a, b and c > 0 I have attempted the problem by expanding the brackets: =36x^2+24xz+4z^2-64 This is the same as (6x+2z)^2-(8)^2 Then subtracting from either 'side' of the quadratic and...

The problem statement: Show that if ##r_1## and ##r_2## are the distinct real roots of ##x^2 + px + 8 = 0##, then ##r_1 + r_2 > 4 \sqrt{2}##. We start by noting that ##r_1 r_2 = 8##. Using this relation, we'll find the minimum value of ##r_1 + r_2##. To minimize ##r_1 + r_2##, we need to...

Hi - I'm trying to figure out the specific steps in a math textbook. I'm trying to figure out how the textbook did its algebra here with a quadratic formula to find an inverse of a function: Sadly there's a step I'm supposed to know by now in the simplification algebra in there 3 steps...

How to find if a quadratic expression of the form 4x2 + 4.n.x - P ......(x,n and P are natural number) is a perfect square. For example, 4x2 + 64x - 31 Thanks.

Homework Statement Homework Equations Quadratic discriminant The Attempt at a Solution I did b^2 -4ac>=0, but the algebra becomes prohibitively difficult.

I have two table, first one changes quadratically and second table changes linearly. 46 ... 55 90 ... 57 142 ... 59 202 ... 61 270 ... 63 346 ... 65 430 ... 67 522 ... 69 622 ... 71 730 ... 73 846 ... 75 970 ... 77 and so...

I derived a relation between the product of two linear polynomials and the square of their average. It can be used to solve any quadratic equation. Will this help me getting into a top university?

Say there are two quadratic equation 4x2+560x+296 and 4x2+4x Is there a way to know that two quadratic equation have same values. Thank you.

1. Homework Statement Homework EquationsThe Attempt at a Solution I just want some clarification about the rules on solving quadratic equation. My question is coming from my solution for problem 49. Solving problem 49 [/B] Factor: (x−p−q)(√(x−q)+√(x−p))=0 Therefore: x−p−q=0⇒x=p+q this...

Hello! I just want to clarify something about the rules on solving quadratic eqns. I have already solved both problems but in the process of my solution some questions arise. For example in the part of my soltution in problem 48 I have this...

Dx (t)=(B u (t) - v (t))dt B is 7x3 which is known U is 3x1 unknown V is 7x1 which is known dt is step size 0.1 A matrix is equal zero How to design a controller that will drive state to zero

A person, selling a horse for $72, finds that his loss per cent is one-eight of the number of dollars that he paid for the horse; what was the cost price? Can anybody explain the part " loss per cent" and how do I express that algebraically. Thanks!

For relativistic particle dynamics, there are two different approaches to choosing a Lagrangian that give the same equations of motion: The quadratic form is: \mathcal{L} = \frac{m}{2} g_{\mu \nu} U^\mu U^\nu where U^\mu = \frac{d x^\mu}{d \tau} This is for the action that involves...

Hello! I just want to solve this exercise using shortest way possible. $\frac{k-n}{2m+x}+\frac{m-n}{2k+x}=\frac{k+m-2n}{k+m+x}$ Because when I tried it is so lengthy. Maybe you can teach me how to go about it faster. Thanks

Mod note: Changed thread title from "exponential vs linear function" to "quadratic vs linear function. basic question, won't give the full question as i don't need it solved for me, but rather need a conceptual overview of HOW to solve so i can do it myself given two functions A f(n)= c * n B...

a man spent 78 dollars for cigarettes. has the price per box been .50 cents less, he could have had one more box. How many boxes did he buy? Heres what I tried let $y=$ original price per box $y-50=$ new price per box Now, $\frac{780}{y}=$ original number of boxes bought...

Homework Statement Showing all necessary working solve the equation ##iz^2+2z-3i=0## giving your answer in the form ##x+iy## where x and y are real and exact,Homework EquationsThe Attempt at a Solution ##iz^2+2z-3i=0, z^2+(2/i)z-3=0##,using quadratic formula →##(-2/i± √8)/2 , z= √2+1/i## and...

Homework Statement I can't determine where the 40x comes from. From: 4x + 5 = 8√(1 - x) To: 16x^2 +40x + 25 = 64 - 64x^2 Homework Equations √1-x^2 = √1-x *√x+1 The Attempt at a Solution 4x + 5 = 8√(1-x) 4x^2 + 5^2 = (8 - 8x)*(8x + 8) 16x^2 +25 = 64 - 64x^2

Homework Statement Hi, If I have an equation in the form 0 = a*x^2 + b*y^2 + c*x*y + d*x + e*y + c Is it possible to solve this for y? Was hoping just to get a helpful link as this isn't for homework - just a personal project.

Homework Statement Homework Equations none The Attempt at a Solution Is this correct? Thanks.

Hello I've been stuck on this test review question for a few days, and I can't figure it out. Can someone help out? "3x²+12x+c=0, Find solutions for c, where there is 1 real solution, 2 real solutions, and 2 nonreal(complex) solutions"

Homework Statement Hi, I want to generate probing sequence using quadratinc probing technique. If j =4 & table size = 19 & assuming h(K) = 9. Homework Equations h(K), h(K) + 1, h(k) -1, h(k) + 4, h(K) - 4, ... h(K) + (TSIZE -1)power 2 / 4, h(k) - (TSIZE -1) power 2 /4 all divided modulo TSize...

Homework Statement If roots of the equation ##x^2 - 10cx - 11d = 0## are ##a, b## and those of ## x^2 - 10ax - 11 b = 0## are ##c, d## then the value of ##a + b + c + d## is (##a, b, c## and ##d## are distinct numbers)Homework EquationsThe Attempt at a Solution ##a+b=10c## ##c+d=10a## ##...

Homework Statement 0 = -250*(sqrt(x^2+1)-0.8)^2 + 98.1*x + 59.05 Homework EquationsThe Attempt at a Solution I can't figure out how to solve this equation! After expanding the squared term, I still end up with a sqrt(x^2+1) and I can't figure out how to perform a substitution or something to...

Homework Statement If ##\{ x \}## denotes the fractional part of x, then solve: ## \{ x \} + \{ -x \} = x^2 + x -6## It's provided that there are going to be 4 roots of this equation. And two of them will be integers. Homework Equations ## 0 \lt \{ x \} \lt 1~~\text{if}~~x \not\in I## ## \{...

so I've been tasked with this insane question obtain the solution of the following quadratic equation how do I solve this, the 'E' (greek letter),is throwing me out,my complete hazardous guess is 2E(S+Wn)2 <--- 2 is a squared sorry my keyboard skills are lacking also 'tut' any help...