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Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 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.
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.
In mathematics, Euler's identity[note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of can be found using difference of two squares: (since ) Therefore, the linear factors are and . Since the two factors found by this method are complex conjugates, we can use this in ...
Square (algebra) 5⋅5, or 52 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.
Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...
In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers. if and only if n is not of the form for nonnegative integers a and b. The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as ) are. 7, 15, 23, 28, 31, 39 ...