Quadratic Definition and 990 Threads

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...

Homework Statement Sketch the graph of y=x^2 and graph y=1/2(x+4)^2 -5 Homework Equations The Attempt at a Solution So, This is the method I use for vertical compression/expansion Step pattern of a parabola at y=x^2 is 1,3,5 Start at vertex, go out by one, go up by 1...

Homework Statement Dang it! More recurrence relation problems, but this time it’s due to a quadratic equation. Q. In the sequence u1, u2, u3,…,un, u1 = 0, u2 = 3, u3 = 12 and un = a + bn + cn2 Find the values of a, b and c. Homework Equations Provided at back of book…...

Homework Statement Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons 1) I like someone else to work it out in a different method, I wnt to see what other approaches there are 2) Whether mine is taking too long or not. I...

Homework Statement Find the zeros of the quadratic equation? Homework Equations P(x)=4(x+7)^2+(x+7)-3 The Attempt at a Solution I substituted and made it 4u^2+u-3 ?? Then after that I factor then back substitute?? I'm not sure how to back substitute tho.

quadratic inequality--interval notation.. Homework Statement 2x^2<-x+10 Solve inequality and put into interval notation Homework Equations interval notation The Attempt at a Solution I don't even know where to start. I set it equal to zero -2x^2-x+10=0

Hi, I have a problem with splitting x4 + 1 into real quadratic factors. How can this be done? Cheers.

Hi there! I'm working on analyzing some data from an experiment, and you can see a graph of some of the results in the attached .jpg image. I've done both a linear and a quadratic fit on the data points, weighted to error bars (the red lines are the fits). I use percents in the graph, but I'd...

Homework Statement How many solutions does x^{2}\equiv9 mod 7700 have? So my question is if this solution is "legitimate" Solution First notice that 7700=7\cdot11\cdot2^{2}\cdot5^{2} Thus we must solve the system \begin{cases} x^{2}\equiv2 & \left(7\right)\\ x^{2}\equiv9 & \left(11\right)\\...

"Find the rule of correspondence for a quadratic equation that is the same shape as y=x^2, with the only given information being x-intercepts at (-3, 0) and (1, 0)." I cannot for the life of me figure this out, and it's making me feel extremely stupid. I know the answer to the question is y=...

Given an equation in the form 0 = ax2 + bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation? My knowledge of calculus tells me that it is because 0 = ax2 + bx + c is not a...

But seriously, why am I getting the wrong answer here: 4x^2+10x= 5 4x^2+10x - 5 = 0 x=\frac{-10+\sqrt{180}}{8} Answers Incorrect: 3.461 and -23

How do I clear fractions in problems like this and set it up for the quadratic formula: \frac{1}{x-1}+\frac{2}{3}=\frac{2}{x-3} I would like to set this up to be solved with the quadratic formula. Also, is it true that the formula can solve all quadratic equations?

Is there a way to input values within a certain range into my calculator? For example, if I come across something like this: "Draw a curve of y=2x between the values x=+3 and x=-3. From the curve write down the following values: etc, etc, etc" How can I make it graphic w/in a certain range?

Homework Statement A (complex) solution to the quadratic equation of the form z^2 + α z + β = 0, is z = 1 + i. (where α and β are real numerical constants), Write down the other solution and hence determine the values of α and β. Homework Equations The Attempt at a Solution this question...

Homework Statement How do you use the Quadratic Formula to solve First Order ODE? For example, I am given this integration (see attachment at the bottom). Homework Equations The Attempt at a Solution I integrated both sides but I do not know where to go from there (see attachment at the...

Homework Statement For the quadratic form x2-2xy+2yz+z2: a) Find a symmetric matrix that allows the quadratic form to be written as xTAx. b) Determine if the critical point at the origin is a minimum, maximum, or neither. c) Find the points for which the quadratic form achieves its...

Homework Statement Show that if p|(n^2+2an+b) for some n, then ((a^2-b)/p)=1. Homework Equations The Attempt at a Solution Okay, well first I thought that when the book said ((a^2-b)/p)=1, they weren't referring to the Legendre symbol because this is how they have it typed on...

could someone please explain briefly what the problem is with my method of finding such canonical forms. The method we've been taught is to find the canonical form by performing double row/column operations on the matrix representation of quadratic form until we get to a diagonal matrix, and...

I am told that the set of positive definite quadratic forms on R^2 has a metric that turns it into H x R where H is the hyperbolic plane. Can you describe this metric? * As a space the forms are viewed as GL(2,R)/O(2).

Hey, I have a set of quadratic equations in the form of: ax^2 -bxy + cy^2 = d ax^2 -bxz + cz^2 = d ay^2 -byz + cz^2 = d where a,b,c,d are given constants. I am really stuck trying to figure out the values of x,y,z :confused: My previous trial, was attempting to solve it as a...

y^2= 1- 2x^2 im supposed to put it in x^2/a^2 + y^2/b^2 = 1 to find the foci and so forth. when i try to set it up i get 2x^2 + y^2 = 1. I am not sure where to go from here. if i multiply or divide to set the problem up properly the 1 will change and my equation will be messed up. can...

1. An Acapulco diver dives into the sea from a height of 35 m. His height h metres t seconds after leaving the cliff is given by h=-4.9t^2+t+35. How long is it until he reaches the water? How long does it take him to fall from 35 m to 25 m? 2. (-b +/-(sqrt)b^2-4ac)/2b 3. I don't have any work...

Hello. This is 2D with arbitrary orientations. I have a quadratic curve segment defined by 2 end points and another one in between. I can find lots of other points along this curve. I want to find a close-enough elliptic spline. It is defined by 2 end points and the point of intersection...

This is something that's been bothering me for a while... If quadratics are any polynomials that have a degree of 2, then would that make the following equations quadratics (I don't know what all of them are for by the way, they're just equations I'm pulling from my math book which doesn't...

Hi, Everyone: I have a quadratic form q, defined on Z⁴ , and I know the value of q on each of the four basis vectors ( I know q is not linear, and there is a sort of "correction" for non-bilinearity between basis elements , whose values --on all pairs (a,b) of...

Hey all, I was bored as heck with my internet down and started scribbling some random math stuff. I'm sure what I've come up with is old news to most but I found some interesting properties in the following proof and I'm curious what my fellow physicsforums users can come up with to see what...

Homework Statement I'm having major issues working out how to integrate \int\frac{1}{F-Gx+x^{2}}dx , where F and G are constants. Homework Equations The Attempt at a Solution Maple tells me it is an inverse hyperbolic tangent of some description, and I know I have to...

This is what I understand right now: The stark effect is when we perturb a system with hamiltonian H_0 by applying a constant electric field, so that H = H_0 - F D_z where F is the field, aligned in the z direction, and D_z is the z-component of the induced dipole. The first order...

Hi all, Hope some here can help me with this math problem. Given, y1 = ax^2 + b. y2 = cos (y1). where a and b are constants. Is y2 periodic with respect to x.? Visually using example grpah, seems to be periodic. How do u find the exact period of such a function? Thanks in advance...

I want to find value for m for which: 4m2 - 12m > 0 Say I do this algebraically: 4m(m-3) > 0 so m > 0 or m > 3 The answer however is 0 < m and m > 3, I know this as a fact as I have looked graphically. So, my question is, when done algebraically, how do I get 0 < m instead of m...

Homework Statement (a) Estimate the terminal speed of a wooden sphere (density 0.870 g/cm3) falling through air, if its radius is 8.00 cm and its drag coefficient is 0.500. (The density of air is 1.20 kg/m3.) (b) From what height would a freely falling object reach this speed in the absence...

Hi everyone! I need to find the antiderivative(1/(3x^2 + 2)) but am not sure which approach to take. I have tried the following only to arrive at a dead end. 1/3x2+2= .5(1/(3(x/sqrt(2))2+1)= (1/6)(1/((x/sqrt(6))2+(1/3)) Thank you so much!

Homework Statement if roots of the equation ax^2+bx+c=0 be the form of p/(p+1) and (p-1)/p,the the value of (a+b+c)^2 is? Homework Equations The Attempt at a Solution

Prove that t2+2t+1,t2+t, t2+1 is a basis for the space of quadratic polynomials P(2).

Homework Statement I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x). Homework Equations quadratic equation. The Attempt at a Solution I don't think you can use completing square in this, and quadratic equation doesn't really...

Homework Statement Show x^2 + (p+1)/4 \equiv 0 (\mod p) where p \equiv 3 (\mod 4) and p is prime is not solvable.Homework Equations Legendre's and Jacobi symbol, congruencesThe Attempt at a Solution Noticing that x^2 \equiv -(k+1) (\mod p) when p = 4k + 3 ? Now (-1/p)(k+1/p) should tell use...

Homework Statement You throw a penny straight up at a speed of 10m/s from a height of 1 m. 1. what's it position 0.5 seconds after it is released? - i found that value to be 4.775 m 2. how high up does it go? = 6.10 m 3. what is its speed when it hits the ground? =? 4. how long is the...

http://www.cs.odu.edu/~toida/nerzic/content/problem_solving/problem_solving.html example 3 ========================================= Quote Problem: Given that a, b, and c are odd integers, prove that equation ax2 + bx + c = 0 can not have a rational root. Understanding the Problem: This is a...

Hey So i need to write down the first order necessary condition (F.O.C). and i need to find out where does a stationary point exist I know how to solve for the F.O.C when i am given an equation in the standard quadratic polynomial form but here the equation is f(x) = 1/2 xT Qx - cTx where T...

Homework Statement Solve 2kx^2 - (k+1)x + 4 by completing the square Homework Equations 2kx^2 - (k+1)x + 4 The Attempt at a Solution What I have so far: -> x^2 - (k+1/2k)x + 4/2k = 0 -> x^2 - (k+1/2k)x + ((k+1/2k)/2)^2 - ((k+1/2k/2)^2 + 2k = 0 -> x^2 - (k+1/2k)x +...