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Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
Adopted as Teachers' Day, in spoken Thai language "Wan Kru", by a resolution of the government on 21 November 1956. The first Teachers' Day was held in 1957. 16 January marks the enactment of the Teachers Act, Buddhist Era 2488 (1945), which was published in the Government Gazette on 16 January 1945, and came into force 60 days later. Most Thai ...
A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating and , which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]
He then used this lemma to both generate infinitely many (integral) solutions of Pell's equation, given one solution, and state the following theorem: Theorem (Brahmagupta): If the equation x 2 − N y 2 = k {\displaystyle \ x^{2}-Ny^{2}=k} has an integer solution for any one of k = ± 4 , ± 2 , − 1 {\displaystyle \ k=\pm 4,\pm 2,-1} then ...
Solutions of indeterminate quadratic equations (of the type ax 2 + b = y 2). Integer solutions of linear and quadratic indeterminate equations (Kuṭṭaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century. A cyclic Chakravala method for solving indeterminate equations of ...
He presented a method of completing the square to solve quadratic equations, sometimes called Śrīdhara's method or the Hindu method. Because the quadratic formula can be derived by completing the square for a generic quadratic equation with symbolic coefficients, it is called Śrīdharācārya's formula in some places.
In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x 2 + bx + c = 0. with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers.
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems.Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool.