Quadratic Definition and 990 Threads

Find constants $P,\,Q,\,R,\,S, a,\,b$ such that $P(x-a)^2+Q(x-b)^2=5x^2+8x+14$ $R(x-a)^2+S(x-b)^2=x^2+10x+7$

Homework Statement Dear Mentors and PF helpers, I saw this question on a book but couldn't understand one part of it. Here the question: Solve the following inequality I copied the solution as belowHomework Equations The Attempt at a Solution I don't understand why the numerator in step...

Homework Statement A Stark effect experiment is performed on the rubidium D1 line ##(5p \ {}^2P_{1/2} → 5s \ {}^2S_{1/2})## at 780.023 nm. Given that the polarizabilities of the ##5p \ {}^2P_{1/2}## and ##5s \ {}^2S_{1/2}## levels are ##6.86 × 10^{−16}## and ##2.78 × 10^{−16} cm−1 m^2 V^{−2}##...

Homework Statement A player hits a volleyball when it is 4 ft above the ground with an initial vertical velocity of 20 ft/s (equation would be h = -16t2 + 20t + 4). What is the maximum height of the ball? Homework Equations quadratic formula The Attempt at a Solution t = -20 ±√202 - 4(-16)(4)...

hi! i don't quite know how to start solving for this. i understand the problem and what it's asking for but i have no idea how to start solving for it. In a volleyball game, a player from one team spikes the ball over the net when the ball is 10 feet above the court. The spike drives the ball...

Homework Statement 3x^2 + px + 3 = 0, p>0, one root is square of the other, then p=?? [/B]Homework Equations sum of roots = -(coefficient of x)/(coefficient of x^2)[/B] product of roots= constant term/coeffecient of x^2 The Attempt at a Solution ROot 1 = a root 2 = b b=a^2 a.b= 3/3 a^3=1...

Homework Statement Find the derivative of f(X). f(X) = transpose(a) * X * b where: X is nxn a and b are n x 1 ai is the i'th element of a Xnm is the element in row n and column m let transpose(a) = aT let transpose(b) = bT Homework Equations I tried using the product rule...

In class, we've learned: 1.) Factoring and Setting Equal to Zero 2.) Completing the Square 3.) Quadratic Formula Are there any other methods? Thanks.

Find the difference quotient f(x+h)-f(x)/h Where h\ne 0, for the function below f(x)=5x^2+4 Simplify your answer as much as possible. How do I do this?

We learned in class that linear equations have variables that are raised to a highest power of one (x) and that quadratic equations have variables raised to a highest power of two (x^2). What happens when you get equations with variables raised to powers of three (x^3)...four (x^4), etc. etc...

I have pantograph simulation on simulink. The dynamic model of the system is given as a C code. So the input is torque and output is motor angles and velocities. I need to build a QLR controller and to do so I need to come up with state space model of the system, right ? I have the following...

(Reviving an old thread based on a recent request by "mr.smartass#1") A sophisticated answer has to do with the notion that symmetries give rise to conserved quantities. The mathematical expression of this relationship is named Noether's theorem. In this case, the fact that the laws of physics...

Hi, I'm trying to solve this problem and I'm stuck. What I want to do is determine the kind of surface from this equation: x2-2y2-3z2-4xy-2xz-6yz = 11 Matrix representation: 1 -2 -1 -2 -2 -3 -1 -3 -3 I want to find the eigenvalues so I write the characteristic equation like...

Homework Statement A functions is defined as f(x) = ax2 + bx + c, where a, b, c are real numbers. If f(3) = f(– 2) = 0, what is the value of f(0)?Homework EquationsThe Attempt at a Solution As function is 0 at 3, -2, therefore 9a + 3b + c=0 also, 4a -2 b + c=0 c=-6a or c= 6b f(0)=c= 6a...

Homework Statement The Newton iteration formula is based on a Taylor series expansion of the function f(x) around an estimate of the root xn, truncated after the linear term. You are asked to derive a more accurate iteration scheme as follows: Start from the Taylor series expansion of f(x)...

Homework Statement Given x^2 - xy + y^2 = 4(x+y-4) where x, y both are real then the number of pairs (x, y) satisfying the equation will be (A) Only one (B) Two (C) Three (D) No pair Homework EquationsThe Attempt at a Solution The equation can be written as (x-2)^2 + (y-2)^2 + 8 = xy on...

Homework Statement If roots of the equation x^2 - (2n+18)x - n - 11 = 0 (n is an integer) are rational for n=a and n=b then |a-b| is Ans: 3 Homework EquationsThe Attempt at a Solution On substituting a (or b) into the quadratic, the roots are rational. If the roots are rational, then the...

Homework Statement If a, b, c, d are the positive roots of x^4 - 12x^3 - px^2 + qx + 81 = 0, then the area of the quadrilateral formed by x=a, x= -b , y = c and y = -d is: Ans: 36 Homework Equations Vieta, I guess. The Attempt at a Solution I know its going to form a rectangle with sides...

Homework Statement First part of the question (SOLVED) A football player kicks a football so that the angle of incidence is 50 DEG and the initial magnitude of velocity of the ball is 15 m/s. Find the: a) Balls maximum height = 6.7 m b) Time of flight = 2.3 s c) time when the ball reaches...

Homework Statement Dear Mentors and Helpers, Here's the question: Find the possible values of k such that one root of the equation 2x^2 + kx + 9 = 0 is twice the other. Homework Equations My classmate's working: Discriminate > 0 k^2 - (4)(2)(9) > 0 k^2 -72 > 0 [k + sqrt (72)] [k- sqrt(72)] >...

I get why it's a parabola because of the x^2 (for every value of x, y is the square of that number), but why does it shift to the left (and down as well) when I add x?

Homework Statement Consider the following statement: If at all times during a projectile's flight its speed is much less than the terminal speed, the effects of air resistance are usually very small. (a) Without reference to the explicit equations for the magnitude of v t„, explain clearly why...

The equation is: (appears while solving a trigonometric integral using residue theorem) 2Z2+iZ2-6Z+2-i =(2+i)Z2-6Z+(2-i) The roots are: Z1=(2-i) and Z2=(2-i)/5 I can't write the equation in factored form. If I simply write it like this: {z-(2-i)}{5z-(2-i)} It doesn't give the same...

Hi, first off I want to say that I'm new here, so sorry if I do anything wrong. Okay, now to the problem at hand. I know that this is probably really easy and I'm just having one of my moments again, but I can't for the life of me figure out how to do this question: When the radius of a...

Homework Statement Write down the equation of motion for the downward journey of a baseball subject to quadratic drag. Find v as a function of y and, given that the downward journey starts at ymax (given below), show that the speed when the ball returns to the ground is: vterv0 /...

Hi, I don't understand what this question is asking and I have idea how to do it.. any help is very much appreciated! I understand how to complete the square, parabolas and such and the concept of maximum and minimum, I just don't understand this question. A Cattle farmer wants to build a...

Homework Statement A projectile that is subject to quadratic air resistance is thrown vertically up with initial speed v0. (a): Write down the equation of motion for the upward motion and solve it to give v as a function of t. (b): Show that the time to reach th top of the trajectory...

$a^2-bc-8a+7=0$ $b^2+c^2+bc-6a+6=0$ prove:$1\leq a\leq9$

if $x^2 = x+3$ then $x^3 = ??$ Not sure about this would appreciate some help

2x^2+9x = -5 Solved, you can banish this thread now mods. 2x^2+9x = -5 With the given answers, nothing I can come up with matches it. I can't solve it like a normal quadratic, as it gives me no answer that matches those. And I can't factor it. Nothing that adds up to 9, that when you...

Definition/Summary A number n is a quadratic residue mod m if there exists some number a which, squared mod m, gives n. Equations Definition of the Legendre symbol, for any number a and for any odd prime p: \left(\frac ap\right)=\begin{cases} 0&p|a\\ 1&\exists n:n^2\equiv a\pmod p\\...

Definition/Summary A second order polynomial equation in one variable, its general form is ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants, and a \ne 0. Equations ax^2 + bx + c = 0 Extended explanation Since a quadratic equation is a second degree...

Homework Statement The number of integral values of 'a' for which the quadratic equation (x + a) (x + 1991) + 1 = 0 has integral roots are: Homework Equations D = b² - 4ac The Attempt at a Solution What I did was simplify the given equation and I got: x² + (1991 + a)x + (1991a + 1) = 0...

Homework Statement We want to determine the coefficients of a polynomial of the form: ##p(x)=c_{1}x^2 +c_{2}x+c_{3}##The polynomial ##p(x)## must satisfy the constraint ##p(1)=1##. We would also like ##p(x)## to satisfy the following 4 constraints: ##p(−1)=5## ##p(0)=−1## ##p(2)=6##...

Hi! I came across the below thread where a user ('krackers') asked for a proof of the PSF factorising method for quadratic equations. The thread is now closed so I'd like to post my proof here. (The proof considers the simplest case where there are no common factors for a,b,c in the quadratic...

Homework Statement Homework Equations — The Attempt at a Solution Confused with (d) a little. Rocket explodes at ##h=3.85262 ## miles ## -16t^2+1400\sin(\alpha)t=3.852624*5280## ## \alpha=\arcsin\left(\dfrac{3.852624*5280+16t^2}{1400t}\right) ## But what do I do...

I'm having problems getting going on the following question, any help appreciated: As part of his training an athlete usually runs 80 km at a steady speed of \(v\) km h. One day he decided to reduce his speed by 2.5 km h and his run takes him an extra 2h 40 mins. Derive the equation...

Question 1 (a) Solve the quadratic equation x^2 + 4x -5 = 0 (b) Factorise its left hand side. (c) Find interval(s) of x where the left hand side is positive Q1 (a) (x+-1) (x+5) x= 1 x=-5 is that solving the equation? (b) didnt i already factorise the left hand side...

This is one of my weakness in Math, to prove an existing fact. please Tell how to go about doing these problem. 1. Prove that when the discriminant of a quadratic equation with real coefficients is negative, the equation has two imaginary solutions. 2. Prove that when the discriminant of a...

Can a quadratic equation with rational coefficients have one rational root and one irrational root? explain. and Can a quadratic equation with real coefficients have one real root and one imaginary root? Explain. please enlighten me.

Please help me continue this problem A market vendor bought a crate of mangoes for 55 peso. when the crate was opened he found that 4 pieces were not fit to be sold. If he sells the rest at 80 cents more than the buying price, he gets a profit of 8 peso for these remaining mangoes. How many...

please check my work. Pipe A can fill a given tank in 4 hr. If pipe B works alone, it takes 3 hr longer to fill the tank than if pipes A and B act together. How long will it take pipe B working alone? let $x=$ required time for B working together with A $x+3=$ required...

please help me with this $\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$ this is where I can get to when I simplify the the equation above, $x^4-6x^3+12x^2+12x+4=0$

Just over two years ago, I was introduced to the process of completing the square as a way to solve the roots in a quadratic equation. More recently, I've thought about how I could go about extending this to completing the cube. The following short story/proof is the result of during just that...

Homework Statement This is from Cahill's Physical Mathematics. Exercise 5.23. For a \gt 0 and b^{2} – 4ac \lt 0, use a ghost contour to do the integral \int^{\infty}_{-\infty} \frac{1}{ax^{2}+bx+c} \mathrm{d}x Homework Equations Use contour integration and the residue theorem...

Homework Statement I'd like to compute \int \frac{dx}{(ax^2+bx+c)^n}, a,b,c \in \mathbb{R} without resorting to the usual recursion relation method of solution i.e. without using integration by parts. But I'd also like to do it without simplifying ax^2+bx+c into anything...

can you show me a way of solving this problem without considering the discriminant. Find the roots of equation subject to the given condition. $(2m + 1)x^2-4mx = 1-3m$ has equal roots. I solved it using discriminant but I want to know other way of solving it. Thanks!

The solutions ##(x_1, x_2)## for the quadratic equation ##(0=ax^2+bx+c)##: ##x_1 = \frac{-b + \sqrt{b^2-4ac}}{2a}## ##x_2 = \frac{-b - \sqrt{b^2-4ac}}{2a}## Are true if ##x## and ##a##, ##b##, and ##c## ##\in## ##\mathbb{C}## ?

please check my answers if they are correct. these problems are even numbered probs in my books that's why I need somebody to check it. 1. solve for x in terms of other symbols $x^2-2xy-4x-3y^2=0$ using the quadratic formula I get $x=y+2\pm4\sqrt{y^2+y+1}$ 2. what is the width of a strip...

please help me get started with these problems. 1.) It took a faster runner 10 sec longer to run a distance of 1500 ft than it took a slower runner to run a distance of 1000 ft. If the rate of the faster runner was 5ft/sec more than the slower runner, what was the rate of each? 2.) It is...