Power Calculators

x² Quadratic Equation Solver

Solve ax² + bx + c = 0 and calculate the real or complex root components.

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Enter details

Root 1 / Real Part
-1
Root 2 / Real Part
-1
Imaginary Magnitude
2
Discriminant
-16

Also available in our Android app, with charts and full breakdown tables.

📘 About the Quadratic Roots

Solve quadratic equations using the standard quadratic formula.

🧮 Formula

Where

  • a,b,c = coefficients
  • Δ = discriminant
  • real part = -b/(2a)
  • imaginary magnitude = √(-Δ)/(2|a|) when Δ < 0
x = (-b ± √Δ)/(2a), where Δ = b² - 4ac.

✏️ Worked examples

x² - 5x + 6 = 0

You enter
a1
b-5
c6
You get
Root 1 / Real Part3
Root 2 / Real Part2
Imaginary Magnitude0
Discriminant1

The two real roots are 3 and 2.

Try this example →

x² + 2x + 5 = 0

You enter
a1
b2
c5
You get
Root 1 / Real Part-1
Root 2 / Real Part-1
Imaginary Magnitude2
Discriminant-16

The roots have real part -1 and imaginary magnitude 2.

Try this example →

🧭 How to use this calculator

What you enter

  • a
  • b
  • c

What you get

  • Root 1 / Real Part
  • Root 2 / Real Part
  • Imaginary Magnitude
  • Discriminant

💡 Root types

  • Positive discriminant: two real roots.
  • Zero discriminant: one repeated real root.
  • Negative discriminant: complex conjugate roots.

💡 Requirement

  • a must be non-zero.
  • Complex roots are represented by real part plus or minus the imaginary magnitude.

❓ Frequently asked questions

What if the discriminant is negative?

There are no real roots. The calculator gives the real part and imaginary magnitude of the complex pair.