Quadratic Definition and 989 Threads

Hello, I was looking at Riley's solution manual for this specific problem. Along the way, he ended up with a quadratic inequality: If you looked at the image, he said it is given that λ is real, but he asserted that λ has no real roots because of the inequality. Doesn't that mean λ is...

Hello MHB, I have been reading a book on Algebraic Geometry by Reid. On page 15, there's a theorem on Quadratic forms. The book doesn't explicitly define what a Quadratic Form is. From Hoffman & Kunze's book on Linear Algebra I found that given an inner product space $V$ over a field $F$, the...

Here is my previous post! please look at pages 3 - 4 to see what I am talking about. http://mathhelpboards.com/pre-algebra-algebra-2/mathematical-modeling-6006-4.html I figured out how to input the quadratic and logarithmic equations into wolfram, this is what i got. Let me know if its correct...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement I kick a puck of mass m up an incline (angle of slope = θ) with intial speed v0. There is no friction between the puck and the incline, but there is air resistance with magnitude f(v) = cv2. Write down and solve Newton's second law for the puck's velocity as a function of...

Homework Statement In the expression x2 + kx + 12, k is an integer and k < 0. Which of the following is a possible value of k? (A) –13 (B) –12 (C)  –6 (D)   7 Homework Equations I know it uses the a.c method of factorization but don't know how to use it? The Attempt at a...

This is what i got... For option 1 I think it's y=( .5(x-20))^2+20 for x>20 For option 2 I think it's y=30+.5*ln|x-25| for x>25Question: develop equations that model the two replacement pack options (option 1) quedratic model, monthly access fee \$20, included gigabytes 20, cost per...

1) Find the range of values of k such that the function f(x) \equiv k(x+2)^2-(x-1)(x-2) never exceeds 12.5. I've missed several stages of the computation because it is quite lengthy. I hope you get the flow of things. My attempt... (k-1)\left[ x + \left( \frac{4k+3}{k-1} \right)x +...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) Part B 1) A golfer hits a nice iron shot and the ball's height above the ground is given by h(t) = -16t^2 + 80t, where t is the time in seconds since the ball was...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 11) Find the vertex of f(x) = -2x^2 - 8x + 3 algebraically. My Answer: (-2,0) 12) Multiply and simplify: (6 - 5i) (4 + 3i) My Answer: 39 - 2i

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 3) Solve 2x^2 + 4x = 15 by using the quadratic formula. x = -1 +/- 2sqr34 4) Determine whether the given pairs of lines are parallel, perpendicular, or...

Help! Using 3 Points to Find Quadratic Equation in General Form I have a quadratic equation question that I have to solve, but I can't seem to understand it. The question is: "Using points (1,0);(3,0);(0,-6), find the quadratic formula in General Form (ax^2 + bx + c). My teacher says...

Homework Statement a) Let f(x) = ax^2+ bx + c; ∀x ∈ ℝ; where a(≠ 0), b and c ∈ ℝ are constants, (i) Prove that f(k) =(64+(b^2−4ac)^2)/(64a) ; where k = −(b/2a)+(1/a)+(b^2−4ac)/(8a). (ii) Hence, without using graphs and without using your knowledge on quadratic functions and equations, prove...

Could someone please help with this evaluation? Homework Statement -1+/-√11.24/-0.0256 The solutions given for this are -91.9 and 170 and I am truly flabbergasted as to how this instructor achieved these values.

Homework Statement Let ##a,b,c## and ##m \in R^{+}##. Find the range of ##m## (independent of ##a,b## and ##c##) for which at least one of the following equations, ##ax^2+bx+cm=0, bx^2+cx+am=0## and ##cx^2+ax+bm=0## have real roots.Homework Equations The Attempt at a Solution I don't really...

Homework Statement Incomming photon gives half of its energy to an electron during scatering. After scattering, photon is headed ##\phi=120^\circ## according to the original direction. What is the ##\lambda## of the incomming photon? Homework Equations \begin{align} \Delta \lambda &=...

i understand the linear case... example.. #/{(x+5)(x-4)} ----> A/(x+5) + B/(x-4) but i don't understand this.. example.. #/{(x^2+3)(x^2+9)}------>(Ax+B)/{(x-√3)(x+√3)} + (Cx+D)/(x^2+9) first of all... (x-√3)(x+√3)= x^2-3, which is nowhere in the original equation.. it's...

Hi PF, I'm reviewing my notes from class, starting from the very beginning. I'm working on some problems using kinematic equations. Here's one example: a ball falls from 30m (using down as the positive direction) at a velocity of 8 m/s. how long does it take the ball to hit the ground? Why do I...

Homework Statement A ball is thrown at 72km/h speed from top of a building. Building is 125m tall. Homework Equations Distance traveled before it hit the ground is as follows: s = Ut + 0.5 gt^2 The Attempt at a Solution Using quadratic equation: x = -b±b^2 - 4ac / 2a The...

Homework Statement The total number of integers that satisfy the equation x2-4xy+5y2+2y-4=0

Homework Statement The part I'm having problems with is where the last two expressions in 4.13 are equated. Why is xtKx*equal to x*^tKx*? The Attempt at a Solution xtKx* is an inner product and due to symmetry is equal to x*^tKx, but wouldn't equating x to x* mean every <x,y> = <x,x> =...

Hi, I have some confusion about strain energy. When using Lagrange's equations to derive the EOM of vibrating structures, the strain energy is written as : U = q^{T}Kq ; (q is the vector of generalized coordinates, and K is the stiffness matrix). Writing it in this form makes it easy to...

The no. of Real Roots of the equation $\displaystyle \frac{\pi^e}{x-e}+\frac{e^\pi}{x-\pi}+\frac{\pi^{\pi}+e^{e}}{x-\pi-e} = 0$ My try:: Let $\displaystyle f(x) = \frac{\pi^e}{x-e}+\frac{e^\pi}{x-\pi}+\frac{\pi^{\pi}+e^{e}}{x-\pi-e}$ Now we will take a interval $x\in \left(e\;,\pi\right)$...

is there any way to prove or disprove the statement: y=3x^2+3x+1 is prime for all x belongs to natural numbers...

How to find the below quadratic function? y = 0, x = 0 y = 2, x = 1 y = 2, x = -1 Thank you

Any comments or feedback on this theorem and proof are appreciated, including improvements and past publications. Specifically, I'd like to know if someone else has come up with a formula for counting the number of invertible squares modulo N. Definition. If x\in(\mathbb{Z}/N)^\times...

... I've recently retired and it has been a very long time since I was exposed to a classroom learning about quadratic equations. But now finally jobless, I have more time to satisfy some personal curiousities. For my difficulty in not being able to ask a more sensible question, I apologise...

Homework Statement Suppose a,c>0 and b^2-4ac>0 . Explain how you could find x_1, x_2 ε ℝ such that a(x_1) ^2+bx_1x_2+c(x_2)^2<0 . Homework Equations q\begin{pmatrix}x_1\\x_2\end{pmatrix} = a(x_1)^2+bx_1x_2+c(x_2)^2 The Attempt at a Solution I'm not sure where to go with this...

1. I am trying to determine the value of g based on a simple pendulum. I have graphed a scatter plot with the x-axis as L and the y-axis as P. I have 3 different series for different lengths of pendulum. When I try to find a line of best fit I get something like cx^2 + dx + e and this trend...

Solve (m-2)x^2-(m+3)x-2m-1=0.

Homework Statement Your budget for constructing a rectangular enclosure which consists of a high surrounding fence and a lower inside fence that divides the enclosure in half is 2400 dollars. The high fence costs 8 dollars per foot and the low fence costs 4 dollars per foot. Find the...

So you start out with the standard form of a quadratic, $ax^{2}+bx+c=0$, and we know that the solutions are from the quadratic formula: $$x= \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}.$$ Let's assume for the sake of this thread that $a,b,c$ are all real. Now, your mantra when solving equations should...

So here is the question: 2x/7=2x^2

Homework Statement You are the quarterback for the Quinte Saints Football team. You are in the middle of the COSSA gold medal game and you see your receiver is wide open down the field beside the sideline. If he catches the ball, you win the game. However, the biggest guy Joey from the...

Homework Statement The following enclosure is built using 280 m of fencing. If the enclosure has a total area of 2800 m2, what are the dimensions to the nearest tenth? Homework Equations x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a} The Attempt at a Solution Please note that the 3/2w and 5/2w...

Homework Statement You are the quarterback for the Quinte Saints Football team. You are in the middle of the COSSA gold medal game and you see your receiver is wide open down the field beside the sideline. If he catches the ball, you win the game. However, the biggest guy Joey from the...

Here is the question: Here is a link to the question: Solve the quadratic equation? - Yahoo! Answers I have posted a link there so the OP can find my response.

Homework Statement Hey guys, I know there are people on here that can help me figure this out... I have a complex quadratic. The coefficients of the quadratic are a=(1-x) b=x*(u+P/(u*r)) and c=-(u^2 + x*P/r). Using -b/2a +/- sqrt(b^2-4*a*c)/2a I'm trying to analytically reduce this quad eqn...

Homework Statement Homework Equations x(2x^2 - 5) = -1 The Attempt at a Solution This question has been flung at me without any pre-examples how to solve it. I have only dealt with equations like 2x^2 + 5x - 12 = 0. I know that the equation above should be set to zero, but how...

Homework Statement Let A be complex, B be real. Show \left|z^2\right|+ Re(Az)+B=0 only has a solution if and only if \left|A^2\right|\geq4B. Then, assuming the above condition holds, show the solution is a circle or a single point. Homework Equations General quadratic equation I think...

A force F=(cx-3.00x2)i acts on a particle as the particle moves along an x axis, with F in Newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 18 J; at x = 5 m, it is 12 J. Find c. F=ma KE=1/2mv2 I guess I don't understand the relationship between force...

Hi can anyone explain what a quadratic divergence is? and if so how it effects the mass of the scalar field i.e why m^2 = m^2_{0} + \delta m^2, why are these things squared? Also how would this divergence affect the standard model as a natural concept, because from reading books it would...

Homework Statement Let a,b,c be real numbers with a>0 such that the quadratic equation ##ax^2+bcx+b^3+c^3-4abc=0## has non real roots. Let ##P(x)=ax^2+bx+c## and ##Q(x)=ax^2+cx+b##. Which of the following is true? a) ##P(x)>0 \forall x \in R## and ##Q(x)<0 \forall x \in R## b) ##P(x)<0...

Here is the question: Here is a link to the question: Problem Solving - Math? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

Hi, I've been attempting to teach myself mathematics in preparation for further study and I'm currently going through quadratic equations. In case it helps, I'm studying to go back to university, I'll be doing a physics degree with a foundation year. I'm just trying to learn as much math as...

I am required to solve two versions of the similar equation for y(x). I think this would be called a quadratic first order differential equation, but I don't even know if that is the correct name: 1)\frac{dy}{dx}=y - \frac{y^{2}}{10} - 0.9 2)\frac{dy}{dx}=y - \frac{y^{2}}{10} - 5 Confidence...

The purpose of this tutorial is to provide students of algebra with techniques and tips for factoring quadratic expressions. In my experience as a tutor, I have found this can be one of the more difficult and challenging topics for students. I invite anyone with any techniques of their own to...

Hi guys. I've been a lurker for a while, but I've recently become super stumped on this physics question (physics is far from my forté). I've attached the graph of my bouncing ball. First, I had to identify the coefficients and what they mean. I understand that A is acceleration, B is initial...