Zero to Hero Maths

Quadratic Equation – Standard Form and Explanation An equation of the form ax² + bx + c = 0 is called a quadratic equation, where: - a ≠ 0 - a, b, and c are real numbers - The degree of the equation is 2 (because the highest power of x is 2) Why should 'a' not be zero? Let’s understand why the condition a ≠ 0 is important. If we take a = 0, then the equation becomes:     0x² + bx + c = 0     ⇒ bx + c = 0 Now, the equation has become a linear equation, because the highest degree of x is now 1. Hence, it is not a quadratic equation anymore. Can b or c be zero? Yes, b and/or c can be zero in a quadratic equation. Here are a few examples: - If b = 0: The equation becomes ax² + c = 0, Degree of the equation is 2 - If c = 0: The equation becomes ax² + bx = 0 ,Degree of the equation is 2 - If both b = 0 and c = 0: The equation becomes ax² = 0, Degree of the equation is 2 In all these cases, the equation still remains a quadratic equation as long as a ≠ 0. Conclusion To be a...