Find N P Q Calculator

This calculator helps you find the roots of a quadratic equation in the form ax² + bx + c = 0. It calculates the values of n, p, and q which represent the coefficients and roots of the equation. Understanding these values is essential for solving quadratic equations in physics, engineering, and mathematics.

What is Find n p q?

Find n p q refers to solving quadratic equations of the form ax² + bx + c = 0. The values n, p, and q represent:

n - The coefficient of x² (a)
p - The coefficient of x (b)
q - The constant term (c)

The roots of the equation can be found using the quadratic formula:

Quadratic Formula

x = [-b ± √(b² - 4ac)] / (2a)

This formula helps determine the values of x that satisfy the equation, which are the roots of the quadratic equation.

How to Use the Calculator

Enter the coefficient for x² (n) in the first input field.
Enter the coefficient for x (p) in the second input field.
Enter the constant term (q) in the third input field.
Click the "Calculate" button to find the roots of the equation.
Review the results displayed in the result panel.

Note

The calculator will display the roots of the quadratic equation based on the values you enter. If the discriminant (b² - 4ac) is negative, the roots will be complex numbers.

Formula

The quadratic equation is given by:

Quadratic Equation

ax² + bx + c = 0

The roots of the equation can be found using the quadratic formula:

Quadratic Formula

x = [-b ± √(b² - 4ac)] / (2a)

Where:

a is the coefficient of x² (n)
b is the coefficient of x (p)
c is the constant term (q)

Example Calculation

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

Identify the coefficients: a = 1, b = -5, c = 6.
Calculate the discriminant: D = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1.
Find the roots using the quadratic formula:
- x₁ = [-(-5) + √1] / (2*1) = (5 + 1)/2 = 3
- x₂ = [-(-5) - √1] / (2*1) = (5 - 1)/2 = 2

The roots of the equation are x = 3 and x = 2.

Interpreting Results

The results from the calculator will show the roots of the quadratic equation. Here's what each part means:

Root 1 - The first solution to the equation.
Root 2 - The second solution to the equation.
Discriminant - Indicates the nature of the roots:
- Positive: Two distinct real roots
- Zero: One real root (repeated)
- Negative: Two complex conjugate roots

Understanding these results helps in solving problems in physics, engineering, and other scientific fields.

FAQ

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable x, with the general form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

How do I find the roots of a quadratic equation?

You can find the roots using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a). This formula gives you the two possible solutions for x.

What does the discriminant tell me?

The discriminant (b² - 4ac) tells you the nature of the roots:

Positive discriminant: Two distinct real roots
Zero discriminant: One real root (repeated)
Negative discriminant: Two complex conjugate roots