Study Companion

Advanced Math Calculator

Work through algebra homework faster—factor quadratics, convert fractions, and differentiate polynomials with guided steps and saved history.

Enter coefficients a, b, c to compute discriminant and roots for ax² + bx + c = 0.

Quick examples

Results

Discriminant

49

Roots

  • x1 = 5
  • x2 = -2

Step-by-step explanation

  1. Δ = b² - 4ac = 9 - -40 = 49
  2. Two real roots because Δ > 0
  3. x₁ = (-b + √Δ) / (2a) = 5
  4. x₂ = (-b - √Δ) / (2a) = -2

Saved history

Saved results will appear here for quick revision.

    How to use the advanced math calculator

    Solve algebra and calculus problems with guided steps.

    1. Pick a mode

      Select quadratic solver, fraction simplifier, or derivative steps based on your equation.

    2. Enter values

      Provide coefficients, numerators and denominators, or polynomial expressions using x terms.

    3. Review explanations

      Toggle step-by-step mode to see the rules applied and save the solution to history for revision.

    Case study: Exam prep session

    Priya prepares for a calculus quiz while tutoring classmates in algebra.

    Quadratic
    x^2 - 5x + 6 = 0
    Derivative
    s(x) = 4x^3 - 2x^2 + x
    1. Quadratic review

      She solves the quadratic, checks complex root handling, and saves the result for practice.

    2. Fraction refresher

      Simplifies 125/500 to verify discount calculations while helping a friend.

    3. Derivative drill

      Uses derivative mode to confirm the velocity equation and evaluates it at x = 2.

    Study takeaway

    Priya exports the steps to share with classmates and feels confident for the quiz.

    Advanced math FAQs

    Can the quadratic solver handle complex roots?

    Yes. Negative discriminants produce complex conjugate roots with real and imaginary parts.

    What expressions can the derivative tool handle?

    It currently supports polynomials written in x. Trigonometric support will be added later.

    How precise is the fraction simplifier?

    Fractions reduce to lowest terms and show decimal and percent equivalents rounded to six places.

    Further reading

    • Khan Academy algebra
    • Paul's Online Math Notes
    • SymPy documentation

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