Higher MathScalar QuantityNCTB উচ্চতর গণিত অধ্যায় ৫ (সমীকরণ)
Discriminant
Bengali: দ্বিঘাত নিশ্চয়ক•Pronunciation: ডিসক্রিমিন্যান্ট•Symbol: D
Standard Definition:
The algebraic parameter b^2 - 4ac that determines the nature and multiplicity of roots in quadratic equations.
📐 Mathematical Equation, Units & Dimensions
Defining Mathematical Equation
Standard SI Unit
Numerical determinant(সংখ্যাগত সূচক)
Dimensional Analysis
CGS Unit
None
📖 Physical Concept & Comprehensive Explanation
The discriminant determines root geometry: D > 0 gives two distinct real roots (rational if D is a perfect square); D = 0 produces one repeated real root; D < 0 generates complex conjugate roots.
🎯 High-Yield Revision Points
- ✓Formula: D = b^2 - 4ac.
- ✓D > 0: two distinct real roots.
- ✓D = 0: single repeated real root.
- ✓D < 0: complex conjugate roots.
Use Online Solver for Discriminant
Compute step-by-step solutions, verify formulas, and plot interactive diagrams on biggan.me.
❓ Frequently Asked Exam Questions (FAQ)
Common questions in board and competitive entrance examinations
Q1: When are quadratic roots real and equal?
When the discriminant equals zero (b^2 - 4ac = 0).