Lessons 23 · 1 lessons · Sh.A. Alimov, A.R. Xalmukhamedov, M.A. Mirzaakhmedov. Algebra: textbook for Grade 8 of general secondary schools. Revised 4th edition. Tashkent: “O‘qituvchi”, 2019
23
The quadratic equation and its roots
Textbook: pp. 135–138
GoalKnow the definition and coefficients of a quadratic equation; solve simple quadratic equations by factoring.
New words
quadratic equation · kvadrat tenglamaleading coefficient · bosh koeffitsiyentconstant term · ozod hadroot of an equation · tenglamaning ildizi
Explanation
An equation of the form ax² + bx + c = 0, where a, b, c are given numbers, a ≠ 0 and x is the unknown, is called a quadratic equation. Here a is the leading (first) coefficient, b the second coefficient and c the constant term. A value of x that satisfies the equation is its root. Many problems lead to a quadratic equation after algebraic transformations: move all terms to the left and collect like terms. The simplest method is to factor the left side: if (x - x₁)(x - x₂) = 0 then x = x₁ or x = x₂, because a product is zero only if one of the factors is zero. The equation x² = k (k > 0) has two roots, x = ±√k.