How can you determine how many solutions a quadratic function has?

Answer 1

To determine how many solutions a quadratic function has, you can use the discriminant. The discriminant, denoted by Δ (delta), is a part of the quadratic formula and is calculated as follows:

Δ = b² - 4ac

Here, a, b, and c represent the coefficients of the quadratic function written in the standard form ax² + bx + c = 0.

Based on the value of the discriminant, you can determine the number of solutions (also called roots) of the quadratic function:

1. If Δ > 0, the quadratic function has two distinct real solutions.
2. If Δ = 0, the quadratic function has one real solution (a repeated or double root).
3. If Δ < 0, the quadratic function has no real solutions (it has two complex solutions).