Quadratic Trinomial Zeros Calculator

Quadratic trinomial zeros calculator is an essential tool for solving quadratic equations of the form ax² + bx + c = 0. Understanding and mastering these equations is crucial in various fields, including physics, engineering, and computer science.

1. Enter the coefficients a, b, and c of your quadratic equation.
2. Click the “Calculate” button.
3. View the results and chart below.

The quadratic formula to find the roots (zeros) of a quadratic equation is:

x = [-b ± √(b² – 4ac)] / (2a)

The discriminant (b² – 4ac) determines the nature of the roots:

• If it’s positive, there are two distinct real roots.
• If it’s zero, there’s one real root (a repeated root).
• If it’s negative, there are two complex conjugate roots.

Comparison of Quadratic Equations

Equation	Discriminant	Roots
x² – 5x + 6 = 0	1	2, 3
x² + 2x – 3 = 0	16	-3, 1

Roots of x² + 2x – 3 = 0

Value of a	Roots
1	-1, -1
2	-1, -1
3	-1, -1

• Always check the discriminant first to determine the nature of the roots.
• For complex roots, use the Math.sqrt() function to find the square root of the negative discriminant.

What is a quadratic equation?

A quadratic equation is a polynomial equation of degree two, typically written in the form ax² + bx + c = 0, where a, b, and c are coefficients, and a ≠ 0.

What are the roots of a quadratic equation?

The roots of a quadratic equation are the values of x that satisfy the equation. They can be real, repeated, or complex.

Learn more about quadratic equations

Khan Academy’s Algebra section