Quadratic Definition and 965 Threads

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+[SIZE="4"]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...

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...

Homework Statement Given that the roots of x^2+px+q=0 are \alpha and \beta, form an equation whose roots are \frac{1}{\alpha} and \frac{1}{\beta} b) Given that \alpha is a root of the equation x^2=2x-3 show that i)\alpha^3=\alpha-6 ii)\alpha^2-2\alpha^3=9Homework Equations...

Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...

I have a bouncing ball quadratic equation and know that B represents the initial velocity. My question is why does B the initial velocity increase with each bounce of the ball. It seems paradoxical to me, particularly if total energy is decreasing. y=ax^2 + bx + C I have attached...

Arc Length, Irreducible quadratic factors i'm having a hard time seeing this method, and i have to use this method on one of the problems I'm doing to find it's Arc Length. L=\int_{\sqrt{2}}^{\sqrt{1+e^{2}}}\frac{v^{2}dv}{v^{2}-1}} the book suggests to first divide then use a...

[SOLVED] Help on tis quadratic functions question Homework Statement The speed v m/s of a particle traveling from A to B at time t s after leaving A, is given by v =10t-t². the particle starts from rest at A and comes to rest at B. Show that the particle has a speed of 5m/s or greater for...

Homework Statement I am trying to use the quadratic formula for 3x^2 - 12x +11 and I am getting... 12 +/- (sqrt 12)/6 which is supposed to reduce to 6 +/- (sqrt 3)/3 and I can't figure it out...it's very sad!

Ax^2+Bx+C=0 PROGRAM delta1 IMPLICIT NONE REAL :: A,B,C REAL :: DELTA,X1,X2 PRINT *,"Enter the a,b,and c" READ *,A,B,C delta=b**2-4*a*c IF (delta>0)THEN PRINT *,"The roots are real" X1=(-B+SQRT(DELTA))/(2*A) X2=(-B-SQRT(DELTA))/(2*A) PRINT *,"X1 = ",X1,"X2 = ",X2...

can i always the quadratic forumula when i m doing these types of problems. my teacher said i can but sometimes theirs faster ways to do it

Homework Statement Hello everyone! How would you solve a quadratic or nth degree congruence? For example how would I solve: (x^2) + 2x -3 = 0 (mod 8 ) The Attempt at a Solution I know this can be written like: (x^2) + 2x = 3 (mod 8 ) but where would I go from here? and...

Hi, I need to extrapolate vector v_{-1} from v_{0}, v_{1} and v_{2} (see attached pic), so that if v_{2} is on the right/left (2D case for simplicity) of v_{1}-v_{0}, v_{-1} would also be on the right/left. My initial solution was like this: v_{2} - v_{1} = v_{1} - v_{0} + dv, v_{1} - v_{0}...

I have to write the equation of motion for a projectile thrown vertically, under quadratic air resistance. The forces acting on the projectile then are, gravity and the quadratic air resistance. Now, both forces are opposing the projectile, would that mean that if I make gravity negative...

Homework Statement basically I am suppose to linearize d=vit + 1/2at^2 into d/t^2 vs 1/t, t/d vs t^2/d and 1/d vs 1/t and its asking which graphs would be linear and non-linear. Homework Equations d=vit + 1/2at^2 The Attempt at a Solution all i know is that in order to linearize this i...

Homework Statement Hello, I just found a question, and having attempted it many times I get different answers, probably due to my messy working, however I have just tried it twice again and got the same answer, just checking with you guys to see if you think it is correct. Thanks...

Homework Statement Suppose that an object is thrown into the air with an initial upward velocity of Vo meters per second from a height of ho meters above the ground. Homework Equations Then, t seconds later, its height (h(t) meters above the ground is modeled by the function h(t) = -4.9t^2...

Hi everyone, I need help again… on “quadratic inequality”. How come the 1/3 < |x| < 1/2 become 1/3 < x < 1/2 or 1/3 < −x < 1/2? And, this is the original problem of above solutions: 1/9 < x^2 < 1/4. I wasn’t able to find the proof from my calculus book because the book says: 1) |x| =...

This is a simple word problem that I just can't wrap my head around. The answers are 7 and 9: The sum of two numbers is 16, but the sum of their squares is 130. Find the numbers. I am supposed to use a quadratic equation as a means to solve the question, and all I need to do is to create...

Hi, How to find the equation if one root of a quadratic equation is 1 + 3i. Regards, Suganya EasyCalculation ToFocus

Homework Statement I need to find the congruence classes mod (3 + sqrt(-3))/2 in Q[sqrt(-3)]. Homework Equations None known. The Attempt at a Solution I'm not sure how to go about finding these congruence classes. I know that in the regular integers congruences classes mod x are...

Homework Statement For my number theory course, I'm supposed to come up with a definition of congruence in quadratic integers, and define the operations of addition, subtraction, and multiplication. Homework Equations None known. The Attempt at a Solution I honestly have no real...

I'm currently going through some questions and came across quadratic and linear simultaneous equations. Solve the equation: x + y = 1 x^2 + y^2 = 16 I am not interested in the question itself but rather the explanation the book gives me which says after...

Homework Statement How to find the conditions on the coefficients of a quadratic equation for the roots to be outside the unit circle eg bx^2 + x - 1 = 0 where b is a constant How do we find the condition(s) that b must satisfy such that the roots of the quadratic lie outside the unit circle...