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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.)
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.
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2 (y + 1) – 1, a true statement. It is also possible to take the ...
The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [ 1] [ 2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such ...
In the following Diophantine equations, w, x, y, and z are the unknowns and the other letters are given constants: a x + b y = c {\displaystyle ax+by=c} This is a linear Diophantine equation or Bézout's identity . w 3 + x 3 = y 3 + z 3 {\displaystyle w^ {3}+x^ {3}=y^ {3}+z^ {3}} The smallest nontrivial solution in positive integers is 123 + 13 ...
The first use of an equals sign, equivalent to 14 x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557). [ 1] In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. [ 2][ 3] The word equation and its cognates in ...
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...