Understanding the Discriminant | Determining Solutions of Quadratic Equations with Mathematics

discriminant

The discriminant is a concept in mathematics that is used to determine the nature of the solutions (roots) of a quadratic equation

The discriminant is a concept in mathematics that is used to determine the nature of the solutions (roots) of a quadratic equation. It is an expression that is calculated based on the coefficients of the quadratic equation and is represented by the symbol “Δ” (delta).

For a quadratic equation in the form of ax^2 + bx + c = 0, where “a,” “b,” and “c” are coefficients, the discriminant is given by the formula: Δ = b^2 – 4ac.

The value of the discriminant can yield three possible cases regarding the solutions of the quadratic equation:

1. If the discriminant is positive (Δ > 0): This indicates that the quadratic equation has two distinct real solutions. In this case, the equation crosses the x-axis at two separate points.

2. If the discriminant is zero (Δ = 0): This signifies that the quadratic equation has only one real solution. In this scenario, the equation just touches the x-axis at one point.

3. If the discriminant is negative (Δ < 0): This indicates that the quadratic equation does not have any real solutions. In this case, the equation does not intersect the x-axis at all, and the solutions are complex or imaginary. By calculating and examining the discriminant, we can obtain valuable information about the nature and number of solutions a quadratic equation possesses, which has significant applications in various fields of mathematics, physics, engineering, and finance.

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