Consider the equation ax 2 + bx + c = 0, with 0 and let x'e x "be the real roots of this equation. So: Look at the following relationships: Sum of Roots (S) Product of Roots (P) Like, we have We call these relationships Girard relations Check some examples of applying these relationships Determine the sum and root product of the equation 10x 2 + x - 2 = 0.
Category In details
Consider the following situation. Let us be: 1/4> 1/8 but this same inequality can be written in another way where the inequality sign will be the same: (1/2) 2> (1/2) 3 Applying the logarithms on both members and Since the logarithm is a growing function, that is, a larger number corresponds to a larger logarithm, we will have: log ((1/2) 2)> log ((1/2) 3), so by the properties of the logarithms we have: 2 .
Apollonius of Perga, Greek mathematician, called "The Great Geometra". He lived during the last years of the third century until the beginning of the second century BC Author of the famous Treaty of Conical Sections which is considered as one of the main scientific works of antiquity, thus giving him the right to be the most eminent figure of Greek science in the field of pure geometry.
Karen Daltoé Sueli Strelow Maria Montessori Maria Montessori (1870-1952) was born in Italy. He became interested in the study of the sciences, but decided on medicine at the University of Rome. He directed his career to psychiatry and soon became interested in disabled children. “Maria Montessori's great contribution to modern pedagogy was the child's awareness”, realizing that they responded quickly and enthusiastically to the stimuli to perform tasks, exercising motor skills and experiencing autonomy.
Andrew Wiles was born on April 11, 1953, in Cambridge, England. He earned a PhD in mathematics from Cambridge University (1975-1979) under the guidance of Australian John Coates, and was a professor at Princeton. From the 1980s onwards, he established himself as a mathematician for his demonstration (1995) of the most famous mathematical challenge of all time, Fermat's Theorem: Considering the equation xn + yn = zn, Fermat stated that there are no integer values for " x "," y "and" z "that satisfy the equation when" n "is an integer greater than 2.
Jean Bernoulli (or Johann Bernoulli) was a Swiss mathematician. He and his brother Jacques Bernoulli were important disciples of Leibniz. No family in human history has produced as many mathematicians as the Bernoulli family, twelve in all, who have contributed unparalleled in the creation and development of differential and integral calculus.
Eliane Casagrande Tadioto This work was presented to the Pedagogy Course, Modality Degree, for the early years of Elementary School, to the Center for Open and Distance Education of the Institute of Education of the Federal University of Mato Grosso, as part of the evaluation process of the Area. of math.
Jean Carlos Silveira João Luiz Domingues Ribas Abstract This paper aims to make a critical analysis of the discussions about Mathematical Modeling in the teaching process, reports the main themes addressed during the I EPMEM (Paranaense Meeting of Modeling in Mathematics Teaching) held in the city of Londrina -PR.
Rafael Bombelli was an Italian algebraist who was born in January 1526 in Bologna (Italy) and died in 1572, probably in Rome, Italy. Perhaps he was the most important mathematician in Italy, pioneering the study of imaginary numbers. His main five-volume publication on algebra (Algebra) was not published until the year following his death (1573).
Brahmagupta was born in the year 598. He was a mathematician and astronomer from Central India who demonstrated the general solution to the integer quadratic equation (the diophantines) and developed general algebraic methods for application in astronomy in his major work, Brahmasphutasidanta ( 650). In his book, Brahmasphutasidanta, he elevates zero to the category of samkhya (ie numbers) by giving the first rules for calculating with zero: a number multiplied by zero results in zero; the sum and difference of a number with zero results in this number; etc.
Julius Wilhelm Richard Dedekind (1831 - 1916) was one of four children of a Lutheran family from Braunschweig, Germany. He entered Gottingen at nineteen and at twenty-two earned his doctorate with a thesis on calculus, praised even by Gauss. He was a student of Dirichlet and devoted himself to secondary education in Brunswick until the last years of his life.
Albert Girard was born in 1595 in St Mihiel (France) and died on December 8, 1632 in Leiden (Netherlands). He was French, but emigrated as a religious refugee to the Netherlands. He first attended the University of Leiden at the age of 22, where he studied mathematics. However, his first interest was music.
Albert Einstein was born on Friday, March 14, 1879, in Ulm, a thriving city in southern Germany. He was the first and only son of Hermman Einstein and Pauline Koch. Already in the early years of his life, Einstein provoked comments. Her mother was convinced that the shape of her head was unusual and feared she had a mental problem because she was too slow to learn to speak.
Charles Auguste Briot, French mathematician, was born on July 19, 1817 in St. Hippolyte. He was responsible for important contributions in analysis, heat, light and electricity. Despite losing his arm movement due to a childhood accident, he never gave up on being a teacher. In 1838, a year after his arrival in Paris, he began studying at the Ecole Normale Supérieure (1838), where he obtained a doctorate (1842) defending work on the orbit of a solid body around a fixed point.
François Viète was born in the year 1540 in Fontenay-le-Comte, France, and died on December 13, 1603 in Paris. Passionate about algebra, this French mathematician was responsible for introducing the first systematized algebraic notation, as well as contributing to the theory of equations. He became known as the Father of Algebra.
János Bolyai (1802-1860), was born in Kolgsvár on December 15, 1802. His father took special care in his physical and intellectual education in this order so that János's intellect could have a healthy body at his disposal. From an early age, Alnos endowed with an extremely observant spirit revealed superior intellectual abilities.
Lord Kelvin was a British mathematician and physicist. He was born in 1824 and died in 1907. He was born in Belfast, Northern Ireland, by the name of William Thomson. At the age of 68, he would receive the title of nobility of First Baron Kelvin de Largs, for the great importance of his scientific work. At 8, Kelvin was already attending his father's lectures, which was a mathematician.
Interestingly, Isaac Newton was born less than a year after the death of Galileo (who, in turn, was born three days before the death of Michelangelo, one of the greatest Renaissance artists). He was extremely fragile in his early months and soon lost his father, being raised by his grandparents when his mother remarried.
The German mathematician and philosopher Gottfried Wilhelm von Leibniz, was born on July 1, 1646, and died on November 14, 1716. He was a universal genius and a founder of modern science. He anticipated the development of symbolic logic and, independently of Isaac Newton, invented calculus with a higher notation, including symbols for integration and differentiation.
John Nash was born on June 13, 1928 in Bluefield, West Virginia, United States. His father, also John, was an electrical engineer and his mother, Virginia, was a teacher. It was she who encouraged his intellectual curiosity, helping him to obtain a good academic education. As a child, Nash was already solitary and introvert, preferring books to playing with other children.