A quadratic equation is an algebraic equation that contains a variable raised to the second power (x^2) and includes a constant term and a linear term (x). It can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a cannot be equal to 0.
There are several methods for solving a quadratic equation, including factoring, using the quadratic formula, and completing the square. The method used depends on the form of the equation and personal preference. However, the most commonly used method is the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a.
The discriminant is the expression b^2 - 4ac that appears under the square root in the quadratic formula. It helps determine the nature of the solutions to a quadratic equation. If the discriminant is positive, there are two distinct real solutions. If it is zero, there is one real solution. And if it is negative, there are no real solutions.
No, a quadratic equation can only have a maximum of two solutions. This is because a quadratic equation is a second-degree polynomial and, according to the fundamental theorem of algebra, a polynomial of degree n can have a maximum of n distinct solutions.
To check if a given value is a solution to a quadratic equation, simply substitute the value for x in the original equation and see if it satisfies the equation. If the resulting equation is true, then the value is a solution. If not, then it is not a solution.