A quadratic equation is a mathematical expression in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is a variable. It represents a parabola on a graph and can have two solutions.
To solve a quadratic equation, you can use the quadratic formula (x = (-b ± √(b^2 - 4ac)) / 2a) or factor the equation. You can also use the completing the square method or graphing to find the solutions.
A quadratic equation can have two real solutions, two complex solutions, or one repeated solution depending on the value of the discriminant (b^2 - 4ac). If the discriminant is positive, there are two real solutions. If it is negative, there are two complex solutions. And if it is zero, there is one repeated solution.
A quadratic equation with a negative discriminant (b^2 - 4ac < 0) has no real solutions. This means that the parabola does not intersect the x-axis and the equation has no solution.
Yes, the quadratic formula can be used to solve any quadratic equation. However, for some equations, it may be easier to use other methods such as factoring or completing the square.