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In a totally ordered ring, x 2 ≥ 0 for any x. Moreover, x 2 = 0 if and only if x = 0. In a supercommutative algebra where 2 is invertible, the square of any odd element equals zero. If A is a commutative semigroup, then one has , = = =.
For the quadratic function y = x 2 − x − 2, the points where the graph crosses the x-axis, x = −1 and x = 2, are the solutions of the quadratic equation x 2 − x − 2 = 0. The process of completing the square makes use of the algebraic identity + + = (+), which represents a well-defined algorithm that can be used to solve any quadratic ...
Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3.
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Another geometric proof proceeds as follows: We start with the figure shown in the first diagram below, a large square with a smaller square removed from it. The side of the entire square is a, and the side of the small removed square is b. The area of the shaded region is . A cut is made, splitting the region into two rectangular pieces, as ...
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An illustration of the complex plane. The imaginary numbers are on the vertical coordinate axis. Although the Greek mathematician and engineer Heron of Alexandria is noted as the first to present a calculation involving the square root of a negative number, [6] [7] it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572.
A gang member “giggled” as he admitted to kidnapping a young Texas woman at gunpoint and threatening to pimp her out and sell her organs, according to cops.