The Quadratic Formula The Quadratic Formula A Quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the form Ax2 + bx + c = 0 where x represents a variable or an unknown, and a, b, and c are constants with a ≠0. (If a = 0, the equation is a linear equation.) The constants a, b, and c are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square". Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula (given below). Generalization of quadratic equation ;- The formula and its derivation remain correct if the coefficients a, b and c are complex numbers, or more generally members of any field whose characteristic is not 2. (In a field of characteristic 2, the element 2a is zero and it is impossible to divide by it.) in the formula should be understood as "either of the two elements whose square is b2 − 4ac, if such elements exist". In some fields, some elements have no square roots and some have two; only zero has just one square root, except in fields of characteristic 2. Note that even if a field does not contain a square root of some number, there is always a quadratic extension field which does, Know More About :- Power and Roots
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The Quadratic formula was used for several thousand years. The quadratic equation had also changed on occasions. The quadratic formula is: x1,2=(-b/2a) ± (1/2a)(b2-4ac)1/2 Around 2000 years back, the Chinese, Egyptians and Babylonians were already familiar with the area of a square level with length of its every side. By using hay bales, they figured out that they could stack together more nine bales if the length of roof space were wide almost three times. The area of the other complex shapes could also be computed. However, they knew how the sides of the shapes could be worked out and they had faced a little big problem. They should have known how the lengths of the sides are calculated. The shape had to be leveled with total area with the length of sides. The use of Quadratic formula by Egyptians About 1500 years back, Egyptians had not used numbers like they are used today. Words were used for expressing mathematical problems. However the scripture avoided the issue of quadratic equation by solving the areas of every side and constructed a chart. They made something similar to a multiplication table. Computation was made quick and fast. The Egyptians did require computing all sides and shapes every time. They only had to refer to the chart. These tables still exist today. They might be mathematically incorrect but they surely show the beginning of the quadratic formula. The use of Quadratic formula by Babylonians The Babylonians had adopted a diverse way for solving problems. They used numbers instead of words, in contrast with the Egyptians. The numbers used by the Babylonians were a lot more the same like the numbers used today although they were based on a hexadecimal model. Addition and multiplication were easier to do with this system. Around 1000 BC, Babylonian engineers could check theauthenticity of their values. By 400 BC, they discovered a technique called ‘completing the square' for solving problems with areas. Euclid and Pythagoras The first mathematical attempt to invent a quadratic formula was performed in 500 BC by the Pythagoras. Euclid did same in Egypt. He used a simple geometric method and came up with a formula for solving the equation. The Pythagoras had observed that ratios did not add up between area of square and length of sides and there was no other ratio except rational. Euclid had uniquely thought that there would be irrational numbers just like there are rational numbers. He later released a book called ‘Elements' and explained the mathematics for solving quadratic equations in it. However his equation was not using the same formula which is known today, his formula could not calculate a square root. Read More About :- Powers Math
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