Discriminant
b²-4ac
In the context of mathematics, the discriminant is a calculated value that reveals essential information about the properties of a quadratic equation. Essentially, the discriminant is a value obtained by substituting the coefficients of a quadratic equation into a specific formula.
The formula for the discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 – 4ac.
The discriminant is an important value to calculate because it helps us determine the nature of the roots of a quadratic equation. Specifically,
1. If the discriminant is positive and a perfect square, then the quadratic has two real roots.
2. If the discriminant is positive but not a perfect square, then the quadratic has two irrational roots.
3. If the discriminant is zero, then the quadratic has one real root of multiplicity two.
4. If the discriminant is negative, then the quadratic has two complex conjugate roots.
Furthermore, the discriminant can give us other important information about the shape and behavior of parabolas, which are the graphs of quadratic equations. For example, a positive discriminant implies that the parabola intersects the x-axis at two distinct points, while a negative discriminant implies that the parabola does not intersect the x-axis at all.
Overall, the discriminant plays a crucial role in understanding the solutions and behavior of quadratic equations, and it is an important tool for mathematicians, scientists, and engineers in a variety of fields.
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