Discriminant
The discriminant is a mathematical term used in quadratic equations
The discriminant is a mathematical term used in quadratic equations. It represents the expression inside the square root of the quadratic formula. For a quadratic equation in the form ax^2 + bx + c = 0, the discriminant is calculated as:
Discriminant = b^2 – 4ac
The value of the discriminant determines the nature of the solutions for the quadratic equation:
1. If the discriminant is positive (greater than 0), then there are two distinct real solutions. This means the quadratic equation crosses the x-axis at two different points. For example, if the discriminant is 4, we have two real solutions.
2. If the discriminant is zero, then there is one real solution. In this case, the quadratic equation touches the x-axis at a single point. For example, if the discriminant is 0, we have one real solution.
3. If the discriminant is negative (less than 0), then there are no real solutions. In this case, the quadratic equation does not intersect the x-axis and the solutions are complex numbers. For example, if the discriminant is -4, we have two complex solutions.
The discriminant is a useful tool to determine the behavior and nature of the solutions of a quadratic equation without actually finding the solutions themselves. It provides information about the graph and helps in analyzing quadratic functions.
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