Definition:Discriminant of Polynomial/Quadratic Equation
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Definition
Consider the quadratic equation:
- $a x^2 + b x + c = 0$
The expression $b^2 - 4 a c$ is called the discriminant of the equation.
Also see
Note that this is a special case of the general discriminant, although it is important to note that the general formula is given for monic polynomials.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 9$: Solutions of Algebraic Equations: Quadratic Equation: $a x^2 + b x + c = 0$: $9.1$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): discriminant
- 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 5$: Solutions of Algebraic Equations: Quadratic Equation: $a x^2 + b x + c = 0$: $5.1.$