Quadratic Definition and 990 Threads

Alright, so this might be a stupid question, but nevertheless, I ask. I am to consider whether the quadratic form ## P(x,y) = a x + b y + d xy ## can map the integers onto the integers. So through a change of basis, I re-express this as ## P'(u,v) = Au^2 + Bv^2 ## for rational A and B...

1. Determine the equation that represents the relationship between the power and the current when the electric potential difference is 24v and the resistance is 1.5 Ω. 2. Draw a graph of the parabola that corresponds to the equation found in (a). 3. Determine the current needed in order for...

I am looking for some interesting questions on quadratic residues. Anyone know of any resources for an elementary number theory course. I am not looking for drill problems to practice but some important results.

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https://uploads.tapatalk-cdn.com/20180712/28a4bbb89e76d3478ae2fd0825562148.jpg Question 81

What is the most motivating way to introduce quadratic residues? I would like some concrete examples which have an impact. This is for first year undergraduates doing an elementary number theory course. They have done Diophantine equations, solved linear congruences, primitive roots.

I would like to solve this system, which is a sets of non linear quadratic equations, the system needed to be solved can be expressed in general as follow: ϒϒ'C – ϒα = B Where ϒ=(ϒ1,ϒ2,...ϒn)’ is a column vector and ϒ’ its transpose C=(c1,c2,…,cn)’ and B=(b1,b2,…bn)’ are a columns vector And...

Homework Statement Please look at the photo! Homework Equations -x^2+4x=x^2-6x+5 The Attempt at a Solution I got 2x^2-10x+5 but it says it's wrong

So if i take the rules that a straight vertical line drawn through the function with more than one intersection implies it is not a function, to mean that the quadratic equation for a circle is not a function. Furthermore, it also implies a cubic equation, such as x^3 can be a function, because...

Homework Statement Homework Equations Discriminant : b^2-4ac When discriminant = 0 The function has two equal real roots When discriminant < 0 The discriminant has NO real roots When discriminant > 0 The function has 2 different real roots The Attempt at a Solution Why is it so that...

Hello everyone! Apologies if this is a very repetitive question but I have gone through previous forum posts and am still struggling to understand how to identify which equations are appropriate. In the problem below, I have used the kinematic equation of "v = v(i) + at" but my answer is...

Homework Statement Two equations are defined as follows: What is the value of ?Homework Equations Quadratic Format: ##ax^2+bx+c=0## ##y^-x## = ##1/y^x## The Attempt at a Solution I'm not sure In how to attempt this style of question as I know quadratic and equation of...

In a graph , straight line intersects the parabola at(-3,9) & (1, 1) Then the equation is A) x^2-2x+3=0 B) x^2+2x-3=0 C) x^2-3x+2=0 D) x^2-2x-3=0 I know that I can find the answer by substituting the known values to each options, but how to do it the proper way? We need at least three known...

The problem is: f(x)=-2x^2-(1/2) Determine if this statement is true of false: The axis of symmetry is x=-2. What is the axis of symmetry? How can you figure out the axis of symmetry without a b value, since the formula for it is x=-b/2a

The question comes out of a corollary of this theorem: Let B be a symmetric bilinear form on a vector space, V, over a field \mathbb{F}= \mathbb{R} or \mathbb{F}= \mathbb{C}. Then there exists a basis v_{1},\dots, v_{n} such that B(v_{i},v_{j}) = 0 for i\neq j and such that for all...

Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below

1. Homework Statement I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that. I don't have enough X information to find...

<Moderator's note: Moved from a technical forum and thus no template.> Hello I am given the following problem to solve. Identify the quadratic form given by ##-5x^2 + y^2 - z^2 + 4xy + 6xz = 5##. Finally, plot it. I cannot seem to understand what I have to do. The textbook chapter on...

Here a, b, c > 0, and a > bc. Can anyone find the solution of k as a function of (a, b, c)? Thanks.

Consider a free real scalar field. The quadratic term in field of spacetime implies that a universe of these free particles is created, annihilated, recreated, and so on moment by moment. In this video Susskind explains the quadratic term in the Lagrangian youtu.be/D7yXoNAg3J8 (At minute...

Given that $\alpha$ and $\beta$ are the roots of a quadratic equation, evaluate $\frac{1}{\alpha^2}+\frac{1}{\beta^2}$. I find this question to be interesting.

Homework Statement Reformulate the noisy linear regression ## y = X \beta + \epsilon## where ## \epsilon ## is the error as a quadratic program, a second order cone program, and a semidefinite program that solves for ## \beta ##. The purpose of this is to use a solver to study the qualitative...

The answer based on the answer key is 3 seconds. I used the quadratic equation to solve for t. My question is how do we know what sign to use when solving for the final value? For this problem, I had to use the negative sign, but I knew that I needed to use the negative sign because I already...

If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone? @fresh_42 @FactChecker @WWGD

Ok so what am I doing wrong, when i try to put equation 300 = (x+3)(x+2)(1) into Stanford form I get x^2 + 5x - 294 = 0. http://imgur.com/a/N9E83

Ok so what am I doing wrong, when i try to put equation 300 = (x+3)(x+2)(1) into Stanford form I get x^2 + 5x - 294 = 0.

Homework Statement A 1.2 kg block is dropped from a height of 0.5 m above an uncompressed spring. The spring has a spring constant k = 160 N/m and negligible mass. The block strikes the top end of the spring and sticks to it Find the compression of the spring when the speed of the block...

Homework Statement 1)The value of k, so that the equations 2x2+kx-5=0 and x2-3x-4=0 have one root in common 2)The value of m for which one of the roots of x2 is double of one of roots of x2-x+m=0 3)If x2-ax-21=0 and x2-3ax+35 have a root in commom Homework EquationsThe Attempt at a Solution I...

Hey, everyone! I'm helping a friend through his calculus course and we've come across something that has stumped me (see: the title). When I learned calculus, our treatment of the epsilon-delta definition of the limit was, at best, brief. Anyway, here is the problem: Given ##\lim_{x \rightarrow...

This is the last quadratic inequality problem (for now) before moving on to Chapter 3, Section 3.1 THE DEFINITION OF A FUNCTION. Section 2.6 Question 30 Solve the quadratic inequality. (x^4)(x - 2)(x - 16) ≥ 0 Do I set each factor to 0 and solve for x? The values of x are then plotted on...

Section 2.6 Question 68Solve the quadratic inequality. x - [10/(x - 1)] ≥ 4 I begin by subtracting 4 from both sides and then simplify the left hand side, right?

Section 2.6 Question 36Solve the quadratic inequality. x^4 - 25x^2 + 144 ≤ 0 Can someone get me started?

Section 2.6 Question 50Solve the quadratic inequality. (x^2 - 1)/(x^2 + 8x + 15) ≥ 0 x^2 - 1 = (x - 1)(x + 1) Question: Do I solve the numerator or denominator to find the end points? Setting each numerator factor to 0 we get x = 1, x = -1. Factor denominator. x^2 + 8x + 15 = (x + 3)(x +...

Solve the quadratic inequality. 2x/(x - 2) < 3 Multiply both sides by (x - 2). [(x - 2)][2x/(x - 2)] < 3(x - 2) 2x < 3x - 6 2x - 3x < -6 -x < -6 x > 6 Our only end point is x = 6. <----------(6)----------> For (-infinity, 6), let x = 0. In this interval, we get false. For (6...

Solve the quadratic inequality. 2/x < x/2 Multiply both sides by 2x. (2x)*(2/x) < (2x)(x/2) 4 < x^2 4 = x^2 sqrt{4} = sqrt{x^2} -2 = x 2 = x Our end points are -2 and 2. <------(-2)----------(2)-------> For (-infinity, -2), let x = -3. In this interval, we get true. For (-2, 2), let...

Solve the inequality. 2x^2 + 7x + 5 > 0 Factor LHS. 2x^2 + 2x + 5x + 5 > 0 2x(x + 1) + 5(x + 1) > 0 (2x + 5)(x + 1) > 0 2x + 5 = 0 2x = -5 x = -5/2 x + 1 = 0 x = -1 Plot x = -5/2 and x = -1 on a number line. <--------(-5/2)----------(-1)-----------> Pick a number from each interval...

Solve the inequality. x^2 + 4x - 32 < 0 Factor LHS. (x - 4) (x + 8) < 0 x - 4 = 0 x = 4 x + 8 = 0 x = -8 Plot x = 4 and x = -8 on a number line. <--------(-8)----------(4)-----------> Pick a number from each interval. Let x = -10 for (-infinity, -8). Let x = 0 for (-8, 4). Let x = 6...

Homework Statement Homework Equations for equation which has 2 different solutions, D >0 The Attempt at a Solution (1)[/B] D > 0 b^2 - 4ac > 0 3 - 4root2.k > 0 k < 3 / ( 4root 2 ) k < ( 3 root 2 ) /8 has solution of sin tetha and cos tetha sin 0 = 0, cos 0 = 1. when x = 0, and x = 1 -->...

Verify that the numbers 1 + √5 and 1 - √5 both satisfy the equation x^2 - 2x - 4 = 0. I believe the question is asking to plug the given numbers into the quadratic equation and evaluate individually. Let x = 1 + √5 and evaluate. Let x = 1 - √5 and evaluate. Both numbers should yield 0 = 0...

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...

In a certain type of problem, a quadratic equation is formed with the square root of energy being the variable to be found ex: (a*sqrt(E)^2+b*sqrt(E)+c=0). Then they claim since energy (E) is real and positive, only solutions to the quadratic equation in sqrt(E ) being real and positive are...

Homework Statement Find the number of solutions of the equation $$\sqrt {x^2}-\sqrt {(x-1)^2} + \sqrt {(x-2)^2}=\sqrt {5}$$ Answer given: 2 Homework Equations The Attempt at a Solution Completely clueless as to where to start.

Homework Statement I have to take the inverse Laplace of this function (xoms+bxo)/(ms2+bs+k) this can not be broken into partial fractions because it just gives me the same thing I started with. How is this done? This is coming from the laplace of the position function for a harmonic oscillator...

What is the intuitive reasoning for requiring that a Lagrangian describing a free-field contains terms that are at most quadratic in the field? Is it simply because this ensures that the EOM for the field are linear and hence the solutions satisfy the superposition principle implying (at least...

Are there practical uses for the formulas for the sum and product of quadratic roots? I have only seen the topic for these sum and product formulas in one section of any college algebra and intermediate algebra books, and then nothing more. I'm just curious if people, ... scientists or...

Homework Statement When do two quadratic polynomials in ##\mathbb{Z}_3 [x]## generate the same ideal? Homework EquationsThe Attempt at a Solution I feel like they generate the same ideal only when they have the same coefficients, but am not sure how to show this.

Homework Statement I'm having trouble with solving a certain form of an equation with the quadratic formula. I think I'm making a dumb mistake somewhere with my algebra, but I can't seem to find it. Solve with quadratic formula: 1/x^2=4/(0.02-x)^2 Homework Equations 1/x^2=4/(0.02-x)^2 The...

Consider the quadratic equation x^2+px+2p=0 a. Find the discriminant. b. Find the values of p for which there are 2 solutions. c. Find the values of p for which there are no solutions. d. Find the value of p for which there is 1 solution. Please show working out! Thanks.

Ian in London (South).Interests Number Theory. Prime Numbers... Integer iterations of this quadratic expression only yield decimal numbers whose factors end with the digit _1, or _9. Why?