Formulas & tables/Mathematics/Quadratic function/Discriminant

Discriminant

Δ=b2−4ac\Delta=b^2-4ac

Result unit: — (liczba)

What it describes

The discriminant of a quadratic trinomial — its sign determines the number of roots.

Symbols

Δ\Delta
discriminant
a,b,ca, b, c
coefficients

Where it comes from

The discriminant determines the number of roots: Δ>0\Delta>0 — two, Δ=0\Delta=0 — one (double), Δ<0\Delta<0 — none. It is the first step when searching for roots.

When to use it

Always before computing roots; determining the number of solutions of a quadratic equation.

Example

Compute the discriminant of the equation x2−5x+6=0x^2-5x+6=0.
Substitutiona=1a=1, b=−5b=-5, c=6c=6.
ResultΔ=(−5)2−4⋅1⋅6=25−24=1\Delta=(-5)^2-4\cdot1\cdot6=25-24=1.

Related formulas

Roots (zeros) Standard form

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