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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 (in some countries referenced as Bhaskara's formula) is a closed-form expression describing ...
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.)
Solve x 2 ≡ 4 (mod 15). x 2 ≡ 4 (mod 3) has two solutions, 1 and 2; x 2 ≡ 4 (mod 5) has two, 2 and 3. and there are four solutions modulo 15, namely 2, 7, 8, and 13. Solve x 2 ≡ 7 (mod 15). x 2 ≡ 7 (mod 3) has two solutions, 1 and 2; x 2 ≡ 7 (mod 5) has no solutions. and there are no solutions modulo 15. Prime or prime power modulus
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 ...
Completing the square. hide. Animation depicting the process of completing the square. ( Details, animated GIF version) In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form. to the form for some values of h and k . In other words, completing the square places a perfect square trinomial ...
A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k . A solution of a polynomial system is a set of values for the xi s which belong to some algebraically closed field extension K of k ...
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 other ...