QUADRATIC EQUATION Meaning and
Definition
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A quadratic equation is a polynomial equation of the second degree, typically written in the form of ax^2 + bx + c = 0, where "a," "b," and "c" represent real numbers and "x" denotes an unknown variable. It is referred to as "quadratic" because the highest power of the variable in this equation is a square (raised to the second power).
The general form of a quadratic equation encompasses three terms: the "a" term, the "b" term, and the "c" term. These coefficients are crucial in determining the properties and solutions of the equation. The coefficient "a" cannot be zero, as it influences whether the graph of the quadratic opens upward or downward. The coefficient "b" determines the position of the vertex, while "c" represents the constant term.
Quadratic equations may have two, one, or no real solutions, depending on the discriminant, which is calculated as b^2 - 4ac. If the discriminant is positive, there are two distinct real solutions. If the discriminant is zero, there is one real solution, typically referred to as a "double root." On the other hand, if the discriminant is negative, the quadratic equation has no real solutions, yielding complex roots.
Quadratic equations serve a fundamental role in various branches of mathematics, physics, engineering, and other scientific fields. They are commonly used to model real-world situations, such as projectile motion or the behavior of parabolic reflectors. Additionally, they are extensively employed in algebraic problem-solving and play a significant role in the study of quadratic functions, parabolas, and their properties.
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In alg., an equation in which the unknown quantity is a square.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for QUADRATIC EQUATION
- 1uadratic equation
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Etymology of QUADRATIC EQUATION
The word "quadratic" originates from the Latin term "quadratus", which means "square" or "having four sides". This term is derived from the Latin verb "quadrare", meaning "to make square". In mathematics, a quadratic equation refers to an equation of the form ax^2 + bx + c = 0, where the highest power of the variable is a square (squared term). The word "equation" comes from the Latin term "aequatio", which means "equalizing" or "making equal". Therefore, the term "quadratic equation" can be interpreted as an equation that involves making an expression with squared terms equal to zero.
Similar spelling word for QUADRATIC EQUATION
