Quadratic Definition and 989 Threads

My teacher said that, No one knows of any quadratic polynomial that produces an infinite amount of primes. I was thinking could we use a polynomial like x^2+1 and then do a trick similar to Euclids proof of the infinite amount of primes and assume their are only finitely many of them...

Homework Statement Actually, it is told by one of my friend. He asked for the answer of this quadratic equation. m^3-m^2+2=0 Homework Equations m^3-m^2+2=0 The Attempt at a Solution But, I think we need one more equation to solve it. Is there any way to solve it by only...

Before I write anything, I want to apologize because I have no idea how to write equations on this website. This is my first post >.< Also, thank you for helping in advance! Homework Statement A baseball is thrown vertically up with speed vo and is subject to a quadratic drag with magnitude...

Homework Statement Solve for x_1^6+x_2^6 for the following quadratic equation where x_1 and x_2 are the two real roots and x_1 > x_2, without solving the equation. 25x^2-5\sqrt{76}x+15=0 Homework Equations The Attempt at a Solution I tried factoring it and I got...

Wiki defines :In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. Yes,all nice and dandy,I get to then express it in terms of matrices and then I find the eigen values and then find the canonical quadratic form,the usual boring linear algebra...

Homework Statement Find three numbers x,y,z satisfying the following equations: 9x-6y-10z=1 -6x+4y+7z=0 x2+y2+z2=9 Homework Equations The Attempt at a Solution The book suggests that the best approach is to express 2 unknowns in terms of the third unknown from the first 2...

Homework Statement If the roots of x^2 - 2x + 4 = 0 are x1 and x2, what is x1^2 + x2^2? Homework Equations The Attempt at a Solution I don't think these questions can be answered by solving for x only cause there will be no real root(complex number). So I found that x1 + x2 =...

Homework Statement Solve 4y-y2=x for y. The Attempt at a Solution First I tried using the quadratic equation with a=-1 b=4 c=-x y=(-b±(42-4(-1)(-x))(1/2))/2(-1) That got me this far: y=2±(8-2x)(1/2) Then I checked wolfram and now I am confused . Did I not approach this corectly?

Homework Statement Let p be an odd prime. A number ##a\in \mathbb{Z} _{p}^{\ast }## is a quadratic residue if the equation ##x^{2}=a\left( \mod p\right)## has a solution for the unknown x. a. Show that there are exactly (p-1)/2 = quadratic residues, modulo p. The Attempt at a Solution...

My question is: Is there any gain in intuitive mathematical understanding of degrees of freedom from learning their expression using the 'quadratic form' and matrix algebra techniques? This sort of explanation is at least understandable and self-consistent, if not rigorous mathematically...

Homework Statement 3x2-8x-1=0 Homework Equations The Attempt at a Solution So here i attempt to solve the equation...usually the way i go about this is you multiply 3 by -1 you get -3 then i ask myself what multiplies to -3 and adds to -8...after that i am able to solve...

I'm trying to compute the complexity of the quadratic program: $$\displaystyle\min_{\mathbf{X}} (\mathbf{X^TQX +C^TX}) \quad{} \text{subject to} \quad{} \mathbf{A X \leq Y}$$ A is MxN and X is Nx1. Q is positive definite and I'm using the interior point method. Any help in computing the...

Homework Statement Here I have drawn for the following scenarios: Linear Resistance FR = -k\vec{v} a)Free-fall starting from rest, downwards as positive. Now it gets trickier... b)Free-fall starting from rest, upwards as positive. My reasoning is as such: Since the...

Getting ready for linear algebra exam. One question that I got right but not exactly sure why is this: --- Consider the quadratic form Q(x,y,z) = 3x^2 + 3z^2 + 4xy + 4xy + 8xz a) Decide if Q is positive definite, indefinite, etc. b) What point on the surface Q = 1 lies closest to...

Hello, Help! I am stuck again :frown: Okay, I vaguely remember how to factorize the following: 0 = 2x^2 + 5x - 7 The above is easy since all we have to do is find two numbers that when multiplied together gives us -14, and we have to find two numbers that when added together gives us 5...

Homework Statement I am having trouble deriving the velocity equation for an objekt moving vertically upwards. the net force will be m*dv/dt=-mg-kv^2 where k is the drag. At the time t=0 the object's velocity wil be v(0)=v_0

Homework Statement I am having some trouble deriving this velocity equation. I the net force will be [itеx] m * dv/dt = - mg - kv^2 [/itеx] Because the object is moving upwards. At the time t=0 the velocity will be [itеx]v(0)=v_0[/itеx] Homework Equations The Attempt at a Solution

Question 1: A hospital dietitian wishes to prepare a corn-bean vegetable dish which will provide at least 40 grams of carbs, and cost no more than \$0.36 per serving. 28 grams of corn provide 8 grams of carbs and cost \$.04. 30 grams of beans provide 5 grams of carbs and cost \$.03. For taste...

As a student, I was taught 3 ways to solve quadratic equations: i) Factoring ii) Completing the square iii) Applying the quadratic formula, derived by completing the square on the general quadratic in standard form: (1) $\displaystyle ax^2+bx+c=0$ To complete the square, I was taught to...

Prove that 12x-8-3x^2 can never be greater than 4. How do you prove? Do you find he discriminant? But isn't discriminant for roots only not equations?

Homework Statement This is a practice problem for a test on Laplace transforms Find L^-1[ (9s^3+17s^2+66s+45) / (s^2+9)(s+2)^2 ] (L^-1 = inverse laplace transform) Homework Equations From Laplace transform tables: L^-1[ 1 / s-α ] = e^αt L^-1[ s / s^2+ω^2 ] = cos(ωt)...

Lindsay on Facebook writes: I think you mean you got -48 instead of 48, but either way let's go through solving this. x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} Looking at $3x^2+12x+8$ we see that $a=3$, $b=12$ and $c=8$. Plugging that into the above quadratic equation yields. x = \frac{-12 \pm...

Homework Statement So I've worked this problem for awhile. Its a several page of math problem with optimization, legrangians, cramers rule, etc to get to this point. All I need to do now is by hand solve this equation for x and y with the constraint. Homework Equations -0.03x^2 + 40x...

quadratic problem. any other method?? 1. Thie problem statement, all variables and given/known data I was solving this question paper and came across the second problem : http://olympiads.hbcse.tifr.res.in/uploads/rmo-2010 I wanted to solve this one by calculus. I want to know that...

Homework Statement I need to solve 0 = 5x2 - 50x + 125 with solutions x = 5, x = 8. Homework Equations Referencing this thread I arrived at the equation (x - 5)(x - 8) = 5x2 - 50x + 125. Expanding x2 - 13x + 40 = 5x2 - 50x + 125 The Attempt at a Solution I tried to simply...

In wikipedia source: http://en.wikipedia.org/wiki/Quadratic_residue under "composite modulus" section I found the line "On the other hand, if we want to know if there is a solution for x less than some given limit c, this problem is NP-complete;however, this is a fixed-parameter tractable...

for a given range of x in Zn , and n is composite , and ax² + bx + c ≡ 0(mod n) and if (4a,n)=1, I learned that we can solve the congruence by (2ax + b)² ≡ b²-4ac (mod n) ==> y² ≡ z (mod n) So, if n is composite, Sometimes I see, modulo 4an, when do we take 4an and n , how can we...

Solve for $x$: $$4x^2 +4xy - 6y - 9 = 9 $$

Homework Statement Hi, there are several methods to solve an quadratic inequality. 1:by graph 2:if (x-a)(x-b) > 0,(x-a) > 0 and (x-b) > 0 or (x-a) < 0 and (x-b) < 0... 3.Using test value method i.e.Find a and b in the expanded form of (x-a)(x-b) a and b are the critical...

Homework Statement A rectangular parking lot is to be placed with one side along a building where no fence is required. If 1000 yards of wire are available for fencing the other 3 sides of the lot, what is the maximum area the lot may have, and what are the dimensions of the lot of a maximum...

[C++] coding a quadratic root finder with "if statements" //This program solves the qudratic equation #include <iostream> #include<cmath> #include<iomanip> using namespace std; int main() { //Declaring Varibles double coefA; double coefB; double coefC; double x1; double x2; double x3...

Homework Statement 2sqrt (x^2-2), sqrt (4(x^2-2)), x^2. The first 2 formulas are the same thing. However I want to how I would explain the transformation of x^2 to either or of those. I have tried a myriad of things to try get x^2 to any of those other two graphs. A quick answer would be...

Hi, I'm learning statistic. Do you guys know how to calculate quadratic regression by hand, which is: give a data set (x,y), find a parabola f(x)=ax^2+bx+c that minimize the total square errors . I have known how to calculate linear regression. Thanks in advanced.

I have been reading up on Quadratic Equations in my course book, which gives some examples of simple equations and how they are factorised, but can't get my head round this type which is has no examples. x2 - 3x = 0 OK I know it is a quadratic because the term x2 is included. What I require...

Hi, This is perhaps the most rookie question to Mathematics that one could ask, but I have searched for information on the question and found only one source which contained an answer. The answer was that it is because otherwise we wouldn't know what the value of either of the factors is. I...

I have figured out the answer to the question, but I have no idea why and how it works. I have attached a copy of the question. I do apologize I am still having trouble putting into latex, I can install some but not all, so bare with me. So if I multiple out the matrices I get \chi2 +...

Homework Statement Homework Equations The Attempt at a Solution for 24. which is a quadratic function, i understand that you have to exchange the positions of x and y and solve from there...but my question is the inverse function of that quadratic for 24 is a negative number...

Hi everyone(Wink) I have an equation which looks like quadratic to me. 2(x - 5)2 = 32 Can I divide both sides by 2? (x - 5)2 = 16 Can I take the square root? x - 5 = + or - 4 if x = 5 plus 4 = 9 if x = 5 - 4 = 1 Therefore my roots would be; x = 9 or x = 1 Is this method acceptable...

Homework Statement Folks, I wish to construct a quadratic expression from a graph which has the following 2 coordinates. ##(0,0)## and the vertex ##(\alpha h_e,1)## where ##0<\alpha<1## Homework Equations Using the following ##y(x)=a(x-h)^2+k## The Attempt at a Solution...

Working through A Book of Abstract Algebra, I encountered several exercises on roots of polynomials in Z_{n} I was just wondering whether there exists something like a quadratic equation for polynomials of degree 2. If the solutions of the usual quadratic formula happen to be integers, can one...

Homework Statement Find a real quadratic factor of the polynomial: Homework Equations z^{4}+16=0 The Attempt at a Solution I don't know :$

Could anyone please verify with me that I have the right idea in answering the question below. Homework Statement If you know the initial velocity v0 and the initial and final heights y0 and y, you can use x=x0+v0t+(1/2)at^2 to solve for the time t when the object will be at height y. But...

Consider the map f : \mathbb{R}^2 \rightarrow \mathbb{R}^2 defined by (x,y) \mapsto (xy-x^2, xy-y^2) I'm interested in figuring out the range of this function, but I keep thinking myself in circles. What would be a systematic method for approaching something like this?

A is a square matrix. x, b are vectors. I know for Ax=b, that given b, there are an infinite number of pairs (A, x) which satisfy the equation. I'm wondering if the same is true for xAx=b. in particular, what if (x, A, b) are all stochastic vectors/matrices (i.e the entries of b and x add to...

Homework Statement Determine values of a, b, c in the formula ax^2+bx^2 +c that satisfy the conditions: f(0)=0 // Limx->-1 F(x)=3 // limx->2 f(x)=6 The Attempt at a Solution 1. F(0)=0 therefore x=0 so f(0)=a(0)^2+b(0)+c so f(0)=c = 0 so c=0 2. Lim f(x) = 3, x->-1 so...

Hello, My question is as follows. Is it possible to obtain a closed form solution to \displaystyle \max_{\xi\ge 0, \lambda\ge 0}\,\, -\frac{1}{2}\||\xi\||^2 +(\xi,\,\lambda) -\frac{1}{2}\||\lambda\||^2 Here \xi and \lambda are vectors. Thank you.

Hi everyone, Can someone please tell me how to find the factors of the below quadratic equation? 3x^2 - 9x + 4 = 0 I had already tried to find them by using the below method and wasn't able to continue further because of I do not understand. Huygen (3x^2 - 7x + 4) -2x = 0 (3x-4)(x-1)-2x=0

1. i am stuck 2. The profit function is given by P=-2x^2 + 60x - 250, where x units is the quantity and P the total profit. Find the maximum profit and the number of units where maximum profit occurs. Sketch the curve of the profit function. 3. i can't do anything, my brain just jammed...

Homework Statement Use algebra to find the x-intercepts and y-intercept of The graph of y=-x^2/5+x/5+6 this is a parabola. Homework Equations y=-x^2/5+x/5+6The Attempt at a Solution Find the y-intercept , which is substitute 0=x into the equation to find the answer , done that . The problem...

Well suppose for an example of an inequality, |x-1|-|x|+|2x+3| > 2x+4 Well in one of its solutions we were told to apply the method of intervals, rather than taking say what; like 8 combination of signs. For everyone of its intervals(say -3/2 \leqx <0) we are said that 2x+3 \geq 0, x<0...