Quadric Root Calculator

This quadric root calculator helps you find the roots of quadratic equations. Whether you're solving for x in ax² + bx + c = 0, understanding the quadratic formula, or visualizing the roots graphically, this tool provides accurate results and explanations.

What is Quadric Root?

The quadric root refers to the solutions of a quadratic equation, which is a second-degree polynomial equation in the form:

ax² + bx + c = 0

Where a, b, and c are constants, and a ≠ 0. The roots of the equation are the values of x that satisfy the equation. A quadratic equation can have:

Two distinct real roots
One real root (a repeated root)
No real roots (complex roots)

The roots can be found using the quadratic formula, which is derived from completing the square.

Quadratic Formula

The quadratic formula is used to find the roots of any quadratic equation. The formula is:

x = [-b ± √(b² - 4ac)] / (2a)

Where:

a is the coefficient of x²
b is the coefficient of x
c is the constant term
The discriminant (b² - 4ac) 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	No real roots (complex roots)

The calculator uses this formula to compute the roots based on the input values of a, b, and c.

How to Use the Calculator

Enter the coefficient a (must not be zero)
Enter the coefficient b
Enter the constant term c
Click "Calculate" to find the roots
View the results and chart visualization

Note: The calculator handles all cases of quadratic equations, including those with complex roots.

Examples

Example 1: Two Distinct Real Roots

For the equation x² - 5x + 6 = 0:

a = 1
b = -5
c = 6

The roots are x = 2 and x = 3.

Example 2: One Real Root

For the equation x² - 4x + 4 = 0:

a = 1
b = -4
c = 4

The root is x = 2 (repeated).

Example 3: Complex Roots

For the equation x² + x + 1 = 0:

a = 1
b = 1
c = 1

The roots are complex: x = -0.5 ± 0.866i.

FAQ

What is the difference between quadric and quadratic?: The terms "quadric" and "quadratic" are often used interchangeably, but "quadratic" is more commonly used in mathematical contexts. Both refer to equations of degree two.
Can the quadratic formula be used for all quadratic equations?: Yes, the quadratic formula can be used to find the roots of any quadratic equation, regardless of whether the roots are real or complex.
What does the discriminant tell us about the roots?: The discriminant (b² - 4ac) determines the nature of the roots: positive discriminant means two distinct real roots, zero discriminant means one real root, and negative discriminant means complex roots.
How do I know if my quadratic equation has real roots?: Check the discriminant. If b² - 4ac is positive, the equation has two distinct real roots. If it's zero, there's one real root. If it's negative, there are no real roots.
Can I use this calculator for higher-degree polynomials?: No, this calculator is specifically designed for quadratic equations (degree two). For higher-degree polynomials, you would need a different type of calculator.