Results 261 to 270 of about 4,000,497 (331)

The quadratic function and quadratic equations

1985
The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
C. Plumpton, J. E. Hebborn
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Simultaneous Quadratic Equations

The American Mathematical Monthly, 1896
(1896). Simultaneous Quadratic Equations. The American Mathematical Monthly: Vol. 3, No. 5, pp. 137-138.
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Quadratic diophantine equations

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1960
Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations. Tartakowsky’s argument does not lead to any estimate for a positive integer which, though not so excluded, is not represented ...
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On quadratic Boolean equations

Fuzzy Sets and Systems, 1995
Let \(F(x_1, \dots, x_n)\) be a Boolean function and \(F\) a disjunction of terms of the form \(xy\) (i.e. \(F\) is a quadratic truth function). The author presents an algorithm for the solution of the quadratic Boolean equation \(F(x_1, \dots, x_n) = 0\). In a first step a prime-implicant approach is used which determines all possible unknowns \(x_i\)
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The Quadratic Equation

The Mathematics Teacher, 1933
The following method is suggested for the treatment of the quadratic equation in the teaching of algebra. The method makes use of factoring and substitution in their simplest form. If the quadratic is incomplete it can be factored as the difference of two squares, hence given the equation.
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WITHDRAWN: Quadratic Equations

1979
Publisher Summary This chapter discusses quadratic equations. A new method of solving quadratic equations has been developed; this new method is called “completing the square.” Completing the square on a quadratic equation allows obtaining the solutions, regardless of whether the equation can be factored.
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Homogeneous quadratic equations

Mathematika, 1971
Letbe a quadratic form with integral coefficients, and suppose the equationhas a solution in integers x1…, xn, not all 0. It was proved by Cassels [2] that there is such a solution, which satisfies the estimatewhere F = max|fij|. It was later observed by Birch and Davenport [1] that the result can be stated in a slightly more general form.
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Problems: Quadratic Equations

2021
In this chapter, the basic and advanced problems of quadratic equations are presented. To help students study the chapter in the most efficient way, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
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The Babylonian Quadratic Equation

The Mathematical Gazette, 1956
The purpose of this note is to show at a glance the significance of successive steps in the solutions to some of the quadratic equations that have come down in the cuneiform texts as examples of the mathematical instruction given to Babylonian students c. 1600 B.C. It is due to the translations made by O. Neugebauer in Germany and later, with A. Sachs,
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Quadratic Convolution Equations

Journal of Mathematics and Physics, 1942
Not ...
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