A quadratic equation is a polynomial equation of the second degree, meaning it can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The highest power of the variable in a quadratic equation is 2. Quadratic equations can have one or two real solutions, or none at all, depending on the values of a, b, and c. The solutions can be found using the quadratic formula, which states that the values of x that satisfy the equation are given by: x = (-b ± √(b^2 - 4ac)) / (2a) The discriminant (b^2 - 4ac) is used to determine the nature of the solutions. If the discriminant is positive, there are two distinct real solutions. If it is zero, there is one real solution (n2 = -b/2a). If it is negative, there are no real solutions, and the equation represents a pair of complex conjugates. Quadratic equations have many applications in various fields such as physics, engineering, and finance. They can be used to model the behavior of objects in motion, to calculate the roots of functions, or to solve optimization problems. Overall, quadratic equations are important and widely used mathematical tools that have practical applications in many areas of science and technology.
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