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Learn how to solve quadratic equations using the quadratic formula, a closed-form expression that describes the roots of a quadratic function. Explore different methods of deriving the formula, such as completing the square, substitution, and Lagrange resolvents.
A quadratic equation is a polynomial equation of degree two with one unknown variable. It can be written in standard form as ax2 + bx + c = 0, where a, b, and c are known numbers and a ≠ 0.
A polynomial is a mathematical expression involving addition, subtraction, multiplication and exponentiation of variables and coefficients. Learn how to write, classify and manipulate polynomials, and see examples and applications in various fields of mathematics and science.
A quadratic function is a polynomial function defined by a quadratic polynomial, which has degree two in one or more variables. The graph of a univariate quadratic function is a parabola, and the graph of a bivariate quadratic function is a conic section.
Learn how to count the roots of a polynomial by examining sign changes in its coefficients. See the proof, examples, generalizations and applications of this mathematical theorem by René Descartes.
Learn the definition, proof and applications of the polynomial remainder theorem, which states that a polynomial is the sum of a polynomial and the product by a polynomial of lower degree. See examples, formulas and references for this algebraic concept.
The binomial theorem describes the expansion of powers of a binomial, such as (x + y)n, into a sum of terms involving binomial coefficients. Learn the history, statement, examples, and applications of this algebraic formula and its geometric interpretation.
Learn how to express a rational fraction as a sum of a polynomial and fractions with simpler denominators. See the basic principles, examples, methods and applications of partial fraction decomposition in algebra and calculus.