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Quadratic Formula Proof Quadratic Formula Proof 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 :- Roots Math

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Today we are going to see the basic concepts behind different types of equations and how to solve systems of equations. Before moving further, we need to understand the insight of system of equations. A system of equations come with the relationship between two or more functions, which can be used to form a number of real-world situations. It is basically a collection of two or more equations with a same set of unknowns. An equation can be linear or non linear. A system of Linear equations is a collection of linear equations which comes with the same set of variables. Expressions is include one or more variables with signs and symbols of algebra. Algebra is a simple language, used to form mathematical models for real--world situations and to solve this problem that we are not able to solve by using basic arithmetic. For example 3x + 4y = 7z. Now the question arises is that how to simplify expressions? The following is the answer :Firstly remove all the fractions in the equation and then remove the parentheses. Combine all the like terms so that we get all the variables together. Move all the variable terms by adding or subtracting on both sides of the equal sign so the variable terms are all on one side of the equal sign. And finally if there is any multiplication sign then remove it by dividing. Linear systems can be represented in matrix form as the matrix equation: Ax = b. Here where A is the matrix of coefficients, x is the column vector of variables, and b is the column vector of solutions. An example to show a system of equations: 2x + 3y -- z = 1 3x -- 4y -- 7z = 8 -x + 他 y -- 2z = 4 It is a system of three equations in the three variables x, y, z. Differential Equations involve dependent variables and their derivatives with respect to the independent variables or we can say that it is an equation involving derivatives of a function or functions. It plays an important role in various fields like engineering, physics, economics and other sections also. To solve quadratic equation we need to know quadratic formula: general form of quadratic equation is ax2+ bx + c = 0. Read More About :- Solving Equations with Radicals

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