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  Class 10 CBSE Maths – Chapter 4: Quadratic Equations 🔹 Key Concepts and Formulas ✅ What is a Quadratic Equation? A quadratic equation in the variable x x is of the form: a x 2 + b x + c = 0 ax^2 + bx + c = 0 where: a , b , c a, b, c are real numbers a ≠ 0 a ≠ 0 It is called a quadratic equation because the highest exponent of the variable x x is 2. ✅ Standard Forms Pure quadratic: a x 2 + c = 0 ax^2 + c = 0 Quadratic trinomials: a x 2 + b x + c = 0 ax^2 + bx + c = 0 Factorable quadratics: can be written as product of binomials. ✅ Methods of Solving Quadratic Equations Factorisation Method Express as a product of two linear factors Set each factor = 0 and solve Completing the Square Method Convert to perfect square by adding/subtracting a constant Take square root on both sides Quadratic Formula: x = − b ± b 2 − 4 a c 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} This works for all quadratic equations. ✅ Discriminant (D) ...

  Class 10 CBSE Maths – Chapter 2: Polynomials 🔹 Key Concepts and Formulas ✅ What is a Polynomial? A polynomial in one variable x is an expression of the form: a n x n + a n − 1 x n − 1 + … + a 1 x + a 0 a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 Where: a 0 , a 1 , … , a n a_0, a_1, \ldots, a_n are real numbers n is a non-negative integer Each term is called a "monomial" ✅ Types of Polynomials Based on Degree: Zero Polynomial: 0 Constant Polynomial: Degree = 0 Linear Polynomial: Degree = 1 (e.g., 2 x + 3 2x + 3 ) Quadratic Polynomial: Degree = 2 (e.g., x 2 + 2 x + 1 x^2 + 2x + 1 ) Cubic Polynomial: Degree = 3 (e.g., x 3 − 6 x 2 + 11 x − 6 x^3 - 6x^2 + 11x - 6 ) ✅ Degree of a Polynomial: The highest power of the variable in the polynomial. ✅ Zeroes/Roots of a Polynomial: If p ( x ) p(x) is a polynomial, and p ( a ) = 0 p(a) = 0 , then a a is a zero or root of the polynomial. ✅ Geometrical Meaning: The zero of a polynomial ...