Understanding the Discriminant: A Key Factor in Determining Solutions of Quadratic Equations

Discriminant

The discriminant is a term used in mathematics to determine the nature and number of solutions of a quadratic equation

The discriminant is a term used in mathematics to determine the nature and number of solutions of a quadratic equation. For a quadratic equation in the form of ax^2 + bx + c = 0, the discriminant is defined as b^2 – 4ac.

The discriminant can have three possible scenarios:

1. If the discriminant is greater than zero (D > 0): In this case, the quadratic equation has two distinct real solutions. The graph of the quadratic will intersect the x-axis at two different points. For example, if the discriminant is 25, then the equation has two real solutions.

2. If the discriminant is equal to zero (D = 0): In this case, the quadratic equation has one real solution, which is a repeated root. The graph of the quadratic will touch the x-axis at one point. For example, if the discriminant is 0, then the equation has one real solution.

3. If the discriminant is less than zero (D < 0): In this case, the quadratic equation has no real solutions. The graph of the quadratic will not intersect the x-axis at any point. For example, if the discriminant is -9, then the equation has no real solutions. The discriminant is a useful tool in determining the nature of solutions of a quadratic equation without actually solving the equation. It helps in analyzing the behavior of the equation and understanding its graphical representation.

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