Discriminant Calculator

Calculate and analyze the discriminant of quadratic equations

Enter Quadratic Coefficients

For equation ax² + bx + c = 0

Results

Understanding the Discriminant

Key Concepts

  • Discriminant Formula:

    D = b² - 4ac for quadratic equation ax² + bx + c = 0

  • Distinct Real Roots:

    When D > 0, the equation has two different real solutions

  • Repeated Root:

    When D = 0, the equation has one repeated real solution

  • Complex Roots:

    When D < 0, the equation has two complex solutions

Applications

  • Graphical Analysis:

    Determine where a parabola intersects the x-axis

  • Engineering:

    Analyze vibrations and oscillatory systems

  • Mathematics:

    Study the nature of quadratic equations

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