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[10] An important Internet protocol, the Border Gateway Protocol, was sketched out in 1989 by engineers on the back of "three ketchup-stained napkins", and is still known as the three-napkin protocol. [11] UTF-8, the dominant character encoding for the World Wide Web, [12] was designed by Ken Thompson and Rob Pike on a placemat. [13]
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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.
Format for Additional Mathematics Exam based on the Malaysia Certificate of Education is as follows: Paper 1 (Duration: 2 Hours): Questions are categorised into Sections A and B and are tested based on the student's knowledge to grasp the concepts and formulae learned during their 2 years of learning. Section A consists of 12 questions in which ...
The origin of the class of such problems has been attributed to the Indian mathematician Mahāvīra in chapter VI, § 131 1 ⁄ 2, 132 1 ⁄ 2 of his Ganita-sara-sangraha (“Compendium of the Essence of Mathematics”), circa 850CE, which dealt with serial division of fruit and flowers with specified remainders. [1]
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
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Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.