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Solving Quadratic Equations definitions

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  • Quadratic Equation
    Polynomial expression with a degree of 2, typically arranged in descending powers and solved for variable values.
  • Standard Form
    Arrangement of terms as ax² + bx + c = 0, with all terms on one side and powers decreasing from left to right.
  • Coefficient
    Numerical factor multiplying a variable in an equation, crucial for identifying a, b, and c in quadratic expressions.
  • Constant Term
    Standalone number in an equation, representing c in the standard form and affecting solution types.
  • Leading Coefficient
    First numerical factor in a quadratic equation, associated with the x² term and influencing solution methods.
  • Factoring
    Process of rewriting a quadratic as a product of binomials, enabling solutions by setting each factor to zero.
  • Square Root Property
    Technique for solving equations in the form (x + a)² = k by taking both positive and negative square roots.
  • Completing the Square
    Method of transforming a quadratic into a perfect square trinomial, allowing use of the square root property.
  • Quadratic Formula
    Universal solution method for any quadratic equation, using a, b, and c in x = (-b ± √(b² - 4ac)) / (2a).
  • Discriminant
    Expression b² - 4ac under the square root in the quadratic formula, determining the nature of the roots.
  • Complex Root
    Solution involving the imaginary unit, arising when the discriminant is negative in a quadratic equation.
  • Radical
    Root expression, often appearing in solutions when the discriminant is not a perfect square.
  • Perfect Square Trinomial
    Quadratic expression that factors into (x + a)², created during the completing the square process.
  • Binomial
    Algebraic expression with two terms, commonly resulting from factoring quadratic equations.
  • Degree
    Highest power of the variable in a polynomial, indicating the equation type and solution approach.