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Find N X P and Q Calculator

Reviewed by Calculator Editorial Team

Quadratic equations are fundamental in algebra and appear in many real-world problems. This calculator helps you find the values of n, x, p, and q in quadratic equations by solving for the roots using the quadratic formula.

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation in the form:

General form of a quadratic equation

ax² + bx + c = 0

Where:

  • a, b, and c are coefficients
  • x is the variable
  • a ≠ 0 (otherwise it's not quadratic)

Quadratic equations can have two real roots, one real root, or two complex roots depending on the discriminant (b² - 4ac).

How to use the calculator

  1. Enter the coefficients a, b, and c in the calculator form
  2. Click "Calculate" to solve the equation
  3. View the roots (x values) and discriminant
  4. Interpret the results based on the discriminant value

Note

The calculator assumes real coefficients. For complex roots, the calculator will show the complex solutions.

The quadratic formula

The standard method for solving quadratic equations is the quadratic formula:

Quadratic formula

x = [-b ± √(b² - 4ac)] / (2a)

Where:

  • x is the root of the equation
  • √(b² - 4ac) is the discriminant
  • ± indicates both positive and negative roots

The discriminant determines the nature of the roots:

Discriminant Nature of roots
b² - 4ac > 0 Two distinct real roots
b² - 4ac = 0 One real root (repeated)
b² - 4ac < 0 Two complex conjugate roots

Worked example

Let's solve the equation 2x² + 4x - 6 = 0 using the calculator.

  1. Identify coefficients: a = 2, b = 4, c = -6
  2. Calculate discriminant: (4)² - 4(2)(-6) = 16 + 48 = 64
  3. Since discriminant > 0, there are two real roots
  4. Apply quadratic formula:
    • x₁ = [-4 + √64]/4 = (-4 + 8)/4 = 4/4 = 1
    • x₂ = [-4 - √64]/4 = (-4 - 8)/4 = -12/4 = -3

The solutions are x = 1 and x = -3.

FAQ

What if the discriminant is negative?
A negative discriminant means the equation has two complex roots. The calculator will display these as complex numbers.
Can I use this calculator for non-integer coefficients?
Yes, the calculator accepts any real number as coefficients. Just enter the decimal values.
What if a = 0?
The calculator will show an error since a = 0 would make it a linear equation, not quadratic.