Algebra
Quadratic Discriminant Calculator
Determine the nature of roots for any quadratic. Calculate the discriminant (b² - 4ac) to determine if a quadratic equation has real, repeated, or complex roots.
Examples:
Formula Reference
Linear Equation
ax + b = c → x = (c−b)/a
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Discriminant
Δ = b² − 4ac
Vertex Form
y = a(x−h)² + k
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Solution Methodology
01
Identify Coefficients
Extract values a, b, and c from the quadratic equation ax² + bx + c = 0.
02
Compute Discriminant
Calculate Δ = b² - 4ac.
03
Interpret Result
Classify the roots based on the sign of the discriminant.
Common Questions
What does the discriminant tell you?
The discriminant (Δ) tells you the number and type of roots for a quadratic equation. If Δ > 0, there are two real roots. If Δ = 0, there is one real root. If Δ < 0, there are two complex roots.
What is the formula for the discriminant?
For a quadratic equation in the form ax² + bx + c = 0, the discriminant formula is Δ = b² - 4ac. This expression is the part of the quadratic formula under the square root.