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Find The Positive Solution of The Equation Calculator

Reviewed by Calculator Editorial Team

This calculator helps you find the positive solution of quadratic equations. Whether you're a student, teacher, or professional, understanding how to solve quadratic equations is essential in many fields of study and practical applications.

How to Use This Calculator

Using our quadratic equation solver is simple:

  1. Enter the coefficients of your quadratic equation in the form ax² + bx + c = 0.
  2. Click the "Calculate" button to find the solutions.
  3. Review the results and interpretation provided.

The calculator will display both solutions (if they exist) and indicate whether they are real or complex numbers.

Formula Used

The solutions to the quadratic equation ax² + bx + c = 0 are given by:

x = [-b ± √(b² - 4ac)] / (2a)

Where:

  • a, b, c are coefficients of the quadratic equation
  • √(b² - 4ac) is the discriminant

The discriminant determines the nature of the roots:

  • If discriminant > 0: Two distinct real roots
  • If discriminant = 0: One real root (repeated)
  • If discriminant < 0: Two complex conjugate roots

Worked Example

Let's solve the equation x² - 5x + 6 = 0:

  1. Identify coefficients: a = 1, b = -5, c = 6
  2. Calculate discriminant: (-5)² - 4(1)(6) = 25 - 24 = 1
  3. Find solutions: x = [5 ± √1]/2
  4. Positive solution: x = (5 + 1)/2 = 3

In this example, the positive solution is x = 3.

Interpreting Results

When using the calculator, consider these points:

  • The positive solution is the one with the plus sign in the formula.
  • If the discriminant is negative, the equation has no real solutions.
  • For practical applications, ensure your equation is properly formed.

Quadratic equations are fundamental in physics, engineering, and economics for modeling various phenomena.

Frequently Asked Questions

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable, typically in the form ax² + bx + c = 0.

How do I know if my equation has real solutions?

Your equation has real solutions if the discriminant (b² - 4ac) is greater than or equal to zero.

Can I use this calculator for non-integer coefficients?

Yes, the calculator accepts any real numbers as coefficients.