Formulas & tables/Mathematics/Quadratic function/Roots (zeros)

Roots (zeros)

x1,2=−b±Δ2ax_{1,2}=\dfrac{-b\pm\sqrt{\Delta}}{2a}

Result unit: — (liczba)

What it describes

The zeros of a quadratic function (they exist when Δ≥0\Delta\ge 0).

Symbols

x1,x2x_1, x_2
roots
a,ba, b
coefficients
Δ\Delta
discriminant (Δ≥0\Delta\ge 0)

Where it comes from

The formula for the zeros of a quadratic function. The ±\pm sign usually gives two solutions; when Δ=0\Delta=0 they coincide.

When to use it

Solving quadratic equations when Δ≥0\Delta\ge0.

Example

Solve x2−5x+6=0x^2-5x+6=0 (Δ=1\Delta=1).
Substitutionb=−5b=-5, Δ=1\sqrt{\Delta}=1, a=1a=1.
Resultx=5±12⇒x1=3, x2=2x=\dfrac{5\pm1}{2}\Rightarrow x_1=3,\ x_2=2.

Related formulas

Discriminant Vieta's formulas

Found this formula useful? Share it.

It's free — send it to a friend who's revising.

Teaching? Embed this formula on your site.

Free widget — paste it on your school site, blog or notes. It links to the full version.

Teaching a class or tutoring? Guide students in NexTutor →