Quadratic Definition and 989 Threads

If one plots the graph of y = x2-10 x+24 which is a parabola, one observes that it is above the x axis, i.e. y > 0, for two intervals of the real line. (The union of these intervals constitute the set of solutions of the quadratic inequality at the beginning of this question.) Find...

I had a hard time completing the square of some problems. This is what I did with them, I would appreciate if someone could show me the mistake that I am doing and the right process in order to solve these problems. Also, here there is an article about completing the square for anyone that...

Um I don't get this problem, can someone help me get through this step by step please. Air Travel ... A Cessna flies 600 mi at a certain speed. A Beechcraft flies 1000 mi at a speed that is 50 mph fster, but it takes 1 hr longer. Find the speed of each plane ?

Question: Find the coefficient of x^5 in (1+x+x^2)^4. Problem: I have not come across expanding brackets which have x^2. I know how to apply the binomial theorem for (a+b)^n or (1+a)^n but have not come across (1 + ax + ax^2)^n. They are not explained in my textbooks so I was wondering if...

Homework Statement Determine \int\frac{4x^{2}-2x+2}{4x^{2}-4x+3}dx Homework Equations I believe it's necessary to complete the square. The Attempt at a Solution Completing the square for 4x^{2}-4x+3 gives \int\frac{4x^{2}-2x+2}{(x-\frac{1}{2})^2+\frac{1}{2}}dx let...

Show that the equation x2 + (3\alpha - 2)x + \alpha(\alpha - 1) = 0 has real roots for all values of α \in IR. How do i do this? Do i just use the b2 + 4ac \geq 0 ?

Hi folks, I have a function f(t), and I want to find 2nd order polynomials that lower/upper bound f(t) in a fixed interval. For instance, f(t) = exp(2t), 0.1<t<0.4 Find a,b,c so that g(t) = a + b t +c t^2 <f(t) for the given interval I have been googling for the solution, but...

hi, could someone please explain to me the attached excerpt, more specifically, why one has to multiply with the ratio. any ideas will be welcome! thanks

Homework Statement Maximizing the function f(X)=6X-1/2X^2+82. That's it, so 6X-1/2X^2+82 = 82-1/2(X^2-12X) = 82-1/2(X-6)^2+18. So f(X)=100-1/2(X-6)^2. Since (X-6)^2 is positive for any X not =6, than the max is x=6. The part I don't understand is when rearranging the function, how do you...

I know how it works, used to find the unknown variable...been using it since Algebra 2... What do the 'two' answers represent. I know one of them always seems reasonable, but the other one is whack (but it probably has some significance). Can someone give me an example of the...

I also wonder about an other interesting residue relation Let P be a prime, let a^{2^n} be called a cyclic quadratic residue if there is integer m dependent on a such that a^{2^{n + mp}} = a^{2^n} for all integers p \mod P It seems that the sum of all such cylic residues is either 0 or...

Morning everybody!:smile: I'm trying to prove a curious little property of quadratic nonresidues: Let p>5 be a prime number. p|S where S is the sum of the squares of its [p's, that is] quadratic nonresidues. However, I didn't make any headway with this problem. I will very much appreciate...

Hello, I have this problem that I simply cannot nail down. Please help. xi - fixed point of g, g is twice continuously differentiable in a vecinity of xi. z(n+1) = g(g(z(n))) - [g(g(z(n))) - g(z(n))]^2 / [g(g(z(n))) - 2*g(z(n)) + z(n)] Using taylor series expansion of g(z(n)) and...

I have a problem with determining eigenvalues. This is what I've got thus far: Homework Statement Identify and sketch the graph of the quadratic equation 4x² + 10xy + 4y² = 9The Attempt at a Solution We put it in the matrix form: \begin{pmatrix} 4 & 5 \\ 5 & 4 \\ \end{pmatrix} Now we find the...

first part of the question is simple : x^2 - 8x + 11 = 0 solve. using quadratic formula it is 4 +/- root5 second part confuses me, you are given to equation: y - 8y^(1/2) + 11 = 0 and are told to : solve this giving answer in form p +/- Q * root5 i have no idea how to do...

Hello, I'm playing with a set of quadratics x^2 + bx + c, where b is fixed, and c is allowed to be any integer image of a particular exponential function. As a simplistic example, I might have x^2 + 100x + 3 x^2 + 100x + 9 x^2 + 100x + 27 x^2 + 100x + 81 etc. and I'm trying to show that...

http://img337.imageshack.us/img337/8922/problemcmi0.jpg Can anyone explain to me please how this problem is solved ?

http://img151.imageshack.us/img151/5562/updatequicklyte1.jpg how would i solve it using MATLAB ? I tried many times but i didnt get the same answer may anyone help me please ?

can someone show how to simplify \frac{12x+9}{x} = x+9 so that it is in the quadratic form: x^2 -3x -9 = 0 multiplying both sides by x, subtracting both sides by 9 etc. . doesn't give me the quadratic.

Homework Statement If one root of a quadratic equation with rational co-efficient is (2^(1/2)+1) , then find the quadratic equation. Homework Equations x=(-b+d^1/2)/2a d=b^2-4ac The Attempt at a Solution Well, I can't quite understand this question. Please help me to...

I know this is a simple question but for some reason I am getting stumped: Question: x-3=-x^2 atempt: (x^2)+x = 3 x^2 + x + 1/4= 3(4) + 1/4 (x+1/2)^2= 3 root everthing x+1/2= root 3 x=+,- root 3 -1/2

Homework Statement Find the number of integral values of 'k' for which the quadratic equation 2x^2 +kx - 4=0 will have two rational solutions. Homework Equations d=(b^2- 4ac)^(1/2) The Attempt at a Solution If discriminant is a perfect square, then the roots will be rational and...

[SOLVED] Solving quadratic Homework Statement 1a) Solve f(x) = x^2- 4x+m in the form f(x) = (x-a)^2+ b 1b) What is the smallest value f(x) can have? The Attempt at a Solution 1a) Seems simple enough. I set f(x) to 0 and used the completing the square method to solve. Ended up with...

Homework Statement factorize fully: 4x^2 - 12x - 14 Homework Equations The Attempt at a Solution Quadratic equation: (-(-12)+ sqrt(12^2 - (4 * 4 * -14))/ 2 * 4 (12 + sqrt(144 + 224))/8 in the end it became a surd (12+ sqrt(368))/8 Could someone tell me how to factorize this? or is that as...

Just went against the tide of the school and bought an Hp 50g Calculator(love RPN!) however to my dismay the calculator does not appear to do quadratic regression. Now my teacher is pressuring me into using a ti and I can't stand them now that I've gotten used to RPN. Does anyone know how to...

Homework Statement Barry has just solved a quadratic equation. He sees that the roots are rational, real, and unequal. This means the discriminant is a) zero, b) negative, c) a perfect square, d) a non perfect square Homework Equations The Attempt at a Solution I think the...

Hi All, I have a semantics question. Why is the quadratic equation called what it is? A polynomial of degree two is called a quadratic polymonial but I've always associated the root quad to mean four! Thanks in advance. Bob:smile:

[SOLVED] Quadratic Equations How would I find what 'a' and 'q' is in the equation of y=a(x)^2+q when I'm given 2 plots? Example:Find 'a' and 'q' so that a parabola y=ax^2+q passes through each pair. a)(-3,11)and(4,18) if you could give me step by step explanation that would be much...

Since the the discovery of the complex number field resulted in part from efforts to resolve the quadratic formula when b^2 - 4ac was negative, am I right to use the quadratic formula to solve zM^2 + wM - t = 0 in the complex number field even when z, w or t can be fractional powers?

Homework Statement use an appropriate local quadratic approximation to approximate the square root of 36.03 Homework Equations not sure The Attempt at a Solution missed a day of class

Homework Statement Find the eigenvalues and eigenvectors of A = \left(\begin{array}{ccc}5&1&1\\1&3&1\\1&1&3\end{array}\right) The Attempt at a Solution The problem I'm having is finding the eigenvalues for the matrix. In 2d matricies it's not too bad, but in 3d the...

Hey guys. Im having a problem with deciphering positive definite and negative definite for this quadratic form i determined from a matrix. I don't quite understand how to evaluate if its pos def or neg def. From what I see in my notes, q(x,y) > 0 for all x not equal to 0. This doesn't help...

who came up with the Quadratic equation and what is the proof behind it?

[SOLVED] Complex Quadratic Formula Homework Statement Let a, b and c be complex numbers with a not equal to 0. Show that the solution of az^2 + bz + c = 0 are z_1, z_2 = (-b \pm \sqrt(b^2 - 4ac))/(2a) The attempt at a solution I'm assuming z is also complex. Multiplying the equation by...

Homework Statement y^2 - 2y = x^3 + 2x^2 + 2x + 3 Homework Equations The Attempt at a Solution Solve for y How do you solve for y? my book says since that equation is quadratic in y, it can be solved as y = 1 +- sqrt(x^3 + 2x^2 + 2x + 4) but I have no idea how to do that...

An object is coasting on the horizontal axis, in the positive direction and is subject to a drag force f = -bv - cv^{2}. Write down Newton's 2nd Law and solve for v using separation of variables. So first I wrote out Newton's law as: F= m(dv/dt) = -bv - cv^{2} Solving the integral: dt =...

Q: A natural number r between 0 and p-1 is called a quadratic residue modulo p if there exists an integer x such that x^2 is congruent to r modulo p. Find all the quadratic residues modulo 11. I attempted to solve this problem by squaring each of the numbers from x=n=0 to x=n=10...

In college we have been given an exercise about Quadratic Equations, before the actual assignment. We have been told that we need to use three different methods for three different equations. The methods are: The Quadratic Formula, Factorization and Graphical. We have been given three...

Quadratic Question [Urgent] The equation x^{2} + 2px + (3p + 4) = 0, where p is a postitve constant, has equal roots Q) Find the value of p Well if it has equal roots b² - 4ac = 0 so (2p)² - 4(1)(3p + 4) = 0 4p² - 12p - 16 = 0 4(p² - 3p - 4) = 0 4((p+1)(p-4)) = 0 so the...

Regarding \displaystyle{\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}} How should "\displaystyle{\pm}" be treated? I know a square root can be both possitive and negative, but does the quardratic forumla dictate that a possitive root should be added to -b, or does it dictate that a postive root...

Homework Statement x^{2} + 2y^{2} + z^{2} + 2xy + 4xz + 6yz Write down the symmetric matrix A for which the form is expressible as x^{t}Ax where t denotes transpose. Diagonalise each of the forms and in each case find a real non-singular matrix P for which the matrix P^{t}AP is diagonal with...

This should be easy but I've not done this in years and I'm feeling dense: I need to fit a quadratic curve to three constraints, two of which are points, the third is an angle. I've found examples to do this but only if all three constraints are points, so if someone would kindly explain...

Ok this should be pretty simple math for you guys (Sophomore in HS) Given that x-2 is a factor of P(x)=2x^3-3x^2-17x+30, find all other linear factors. I started out doing synthetic division, and got 2x^2-x-19 with remainder -8. Shouldn't the remainder be zero since x-2 is a factor...

Dear forum Please help - I am feeling very useless and depressed as something which worked years ago while at uni now seems to beat me ! I am trying to write a simple script (javascript actually) which calculates the root of a quadratic given two guesses of x (one guess giving y<0, the...

[SOLVED] Quadratic Function Homework Statement solve (f(x)=-3 x^2 + 9 x + 1/4 ) fx=(-3)(x^2-3 x)+1/4 fx=(-3)(x^2-3 x+9/4)+1/4+27/4 fx=(-3)(x^2-3 x+9/4)+28/4 fx=(-3) (x-3/2)^2+7 Homework Equations The Attempt at a Solutionthe solution is already given in the book, but I don't understand why...

hi, i think this one is a bit trickier. for an odd prime number "p", let F_p be the field with "p" elements. i.e. the integers {0,...p-1} with addition and multiplication defined modulo "p". So how many quadratic forms are there on the vector space F^n_p and why? any clues here please?

hi i just wanted a quick explanation of what a symmetric matrix is and what they mean by the quadratic form by the standard basis? (1) for example why is this a symmetric matrix [1 3] [3 2] and what is the quadratic form of the matrix by the standard basis? (2) also how would i go...

I did a pendulum lab and determined that length affected the period. So the values got where: 10 cm = 6.47 s 15 cm = 7.895 s 20 cm = 8.94 s 25 cm = 9.89 s 30 cm = 10.5 s 35 cm = 11.905 s With these values, it seems like graphing this straight as it is results in a linear line, but I...

i learned this a few weeks ago and now i have a project due tomorrow and i want to make sure in doing this right before i make useless graphs... like: (x-1)^2+3 or (x+2)^2 i can't remember how to exponent that ****...

[SOLVED] Quadratic Equations and Inequalities question about properties of quadratic so here is the question graph the function. state the domain and range of the function. F(x)=-2x^2-3x+2 i try and use the axis of symmetry (-b/2a) and then plug that into the original formula to get the...