Understanding the Discriminant: Determining the Nature of Solutions in Quadratic Equations

Discriminant

The discriminant is a mathematical term used in quadratic equations to determine the nature of their roots

The discriminant is a mathematical term used in quadratic equations to determine the nature of their roots. It is denoted by the symbol Δ or D and is calculated using the formula:

Δ = b^2 – 4ac

where a, b, and c are the coefficients of the quadratic equation in the form of ax^2 + bx + c = 0.

By calculating the discriminant, we can determine the type and number of solutions the quadratic equation has:

1. If Δ > 0: This means the discriminant is positive. In this case, the equation has two distinct real roots. The graph of the quadratic equation crosses the x-axis at two distinct points.

2. If Δ = 0: This means the discriminant is equal to zero. In this case, the equation has one real root. The graph of the quadratic equation touches the x-axis at a single point.

3. If Δ < 0: This means the discriminant is negative. In this case, the equation has no real roots. The graph of the quadratic equation does not intersect the x-axis. The discriminant plays an important role in determining the nature of the solutions of quadratic equations, which can provide insights into the behavior of the equation and its graph.

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