# Tagged Questions

Questions on quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

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### Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters

What is the probability that the polynomial has real roots? asked for the probability that the quadratic polynomial $ax^2+bx+c$ has real roots if the parameters $a,b,c$ are exponentially distributed ...
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### How can I find values for which a given expression gives a perfect square?

There have been several posts on this topic on math.se, such as this one with the same title. However all the posts I found contained coefficients to $x^2$, that were perfect squares. I am looking for ...
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### What is relation between a particular root of two polynomials?

We have $$x^3+(m+n+p-1)x^2-((m+n)(1-p)+2p-1-mn)x-(p-1)(m-1)(n-1)=0$$ in which $m,n\ge2, p\ge1$ are natural numbers. All the three roots of this cubic are positive. Let $\lambda$ be the least of them. ...
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### How to use piecewise quadratic interpolation?

I'm attempting to get the hang of quadratic interpolation, in MatLab specifically, and I'm having trouble approaching the process of actually creating the spline equations. For example, I have 9 ...
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### Help solving the quadratic equation $ax^2-4bx+4bc-\frac{d^2}{a}=0$

I have been struggling to solve this quadratic equation in the variable $x$ with integral coefficients: $$ax^2-4bx+4bc-\frac{d^2}{a}=0$$ $a\neq 0$ of course.How do I ensure that $x$ is an integer? ...
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### Parabola Terminology

In Danish we call the two halves of a parabola that goes out to each side from the vertex branches like branches on a tree. Is there a name for them in English? Are they just called halves or maybe ...
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### How do you the roots of functions that are not quadratics?

I was asked to consider the equation $(x-3)(x+3)^2=c$ I have been asked to find the values of C in which the equation has: three distinct roots only one real root a double root and a single root ...
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### Why the quadrature formula is exact one not an approximation?

I am reading this material on the algorithm of calculating the centroid of a polyhedron. I am confused by the last step of the deduction: The three coordinates of the centroid can be obtained: ...
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### Taylor expansion need help understanding.

I am at the moment reading a paper (SURF) and trying to understand what is happening here and how the things works as it does.... a non maximum supression is performed on the scale space ...
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### Lagrange multiplier expression

I would like to solve the following optimization problem using the gradient ascend method: \begin{array}{ll} \text{maximize}_{\theta} & \theta^TQ_1\theta + b_1\\ \text{subject to} & \theta^...
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### Extraction of quadratic terms with state-space representation

I am having trouble with transforming the dynamics of a 4DOF gyroscope to a neat state-space representation. The system has the following set of equations: $T_i + f_i(\omega, \alpha) = 0;\;i:1-4$ . ...
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### Does $2^2=4$ imply $2=\pm \sqrt{4}$?

I read the square root property from the book, College Algebra by Raymond A Barnett and Micheal R Ziegler that, The square root property says, If $A^2=C$ then $A=\pm \sqrt{C}$ I took the ...
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### $A(x+p)²-B(x-p)²=y$, historical/math reference

I'm trying to build a reminder of all that I found about the quadratic function over the years. Here I came across this form of quadratic equation that I did not know: A(x+p)²-B(x-p)²=y I have no ...
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### can someone break this quad formula down for me?

Can someone explain how this person yield the stuff on the right side using quad formula?
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### Derivative of quadratic form involving singularity

This might be a silly question, but i have been really curious about the following: Consider the following function seen thru a single variable, say $\alpha$: f(\alpha) = \mathbf{x}^...
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### Trigonometric roots of a cubic

Let the product of the sines of the angles of the triangle is $\frac{2}{3}$ and the product of their cosines is $\frac{1}{9}.$ If $\tan A$ , $\tan B$ and $\tan C$ are the roots of the cubic, find the ...
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### Not sure what is meant by Quadratic Matrix. Is this an academic, or domain-specific term?

I'm not a mathematician, and the last time I studied maths was a good eight years ago. I'm going through a book called 'An Introduction to Recommender Systems', and in ...
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### How to constrain the linear least squares fit of a quadratic polynomial with known constraints

How to constrain this fit I have some function , $f(x) = a x^2+b x+c$ , with the constraints $a<0$ and $c = \frac{b^2}{4a}+\frac{1}{2}ln(\frac{-a}{\pi})$ I have measured $f(x)$ for some $x$. Can ...
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### Solve quadratic vector equation, with variable hidden inside scalar

Let $\vec{f}$ $m\times 1$ unknown vector, given $n\times 1$ vector $\vec{F}$, $n\times m$ matrix A ($n<m$), nonzero vector $\vec{v}$ from the nullspace of A ($Av=0$), non-invertible symmetric ...
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### Taylor's formula and its quadratic term

I struggle with the following problem: For a function $$f: \mathbb{C} \rightarrow \mathbb{R}~,$$ $f$ attains its maximum for $z_0= e^{i\pi/3}$, $f(z_0)=F_{max}.$ Assume we may use Taylor's theorem (...
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### If you are using piecewise quadratic polynomials to approximate the function $f (x) = \ln x$ on the interval $[1, 2]$

If you are using piecewise quadratic polynomials to approximate the function $f (x) = \ln x$ on the interval $[1, 2]$ and expect the maximum error to be smaller than $10^{-6}$, how many subintervals ...
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### Linear Algebra and Quadratic Equations

I'm just wondering if Linear Algebra is concerned only with Linear equations? Can quadratic equations(or any higher power) also be considered under Linear Algebra? What does the term Linear stand for?
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### solving quadratic equation in GF(2^m)

I am trying to implement Elliptic Curve Cryptography on software in GF(2^m). To do this, I need to be able to solve a quadratic equation, namely $x^2 + x = c$. After a lot of research, I know the ...