Discriminant
b²-4ac
In mathematics, the discriminant is a term used in algebra that is used to determine the number and type of roots of a quadratic equation. Quadratic equations are those that have an x² term and a constant term, and the standard form is ax² + bx + c = 0, where a, b, and c are constants.
The discriminant is given by the expression b² – 4ac. It is often denoted by Δ (delta) and represents the value inside the square root in the quadratic formula:
x = (-b ± √Δ) / 2a
If the discriminant is positive, then the quadratic equation has two distinct real roots. If it is negative, then the equation has two complex conjugate roots. Finally, if the discriminant is equal to zero, then the equation has a single real root with multiplicity two.
Knowing the discriminant can help us determine the nature of the roots of a quadratic equation without actually solving the equation. This is especially useful in cases where it is difficult or impractical to solve the equation directly, or when we only need to know the general nature of the roots rather than their specific values.
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