Final answer:
An equation that can be written in the general form ax² + bx + c = 0, a ≠ 0 is called a quadratic equation. The solutions to a quadratic equation can be calculated using the quadratic formula.
Step-by-step explanation:
An equation that can be written in the general form ax² + bx + c = 0, where a ≠ 0, is called a quadratic equation. The general form of a quadratic equation allows us to easily identify its coefficients (a, b, c) and use them to find the solutions or roots of the equation.
The solutions to a quadratic equation can be calculated using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). By substituting the coefficients (a, b, c) from the equation into the quadratic formula, we can find the values of x.
For example, if we have the equation x² + 5x + 6 = 0, we can identify that a = 1, b = 5, and c = 6. Plugging these values into the quadratic formula, we get x = (-5 ± √(5² - 4(1)(6))) / (2(1)). Solving this equation gives us two values for x: x = -2 and x = -3.