How this Quadratic Calculator Works
This tool solves quadratic equations, which are polynomial equations of the second degree. The standard form is ax² + bx + c = 0, where 'x' is the unknown variable and a, b, and c are coefficients.
The Quadratic Formula
To find the value(s) of x, we use the famous quadratic formula. This formula can solve any quadratic equation, even if it cannot be factored easily.
x = [ -b ± √(b² - 4ac) ] / 2a
The Discriminant (Δ)
The term inside the square root, b² - 4ac, is called the "Discriminant." It tells us the nature of the roots without even calculating them fully:
- Positive (> 0): Two distinct real solutions. The graph crosses the x-axis twice.
- Zero (= 0): One real solution (a "double root"). The vertex of the parabola touches the x-axis.
- Negative (< 0): Two complex solutions (involving imaginary numbers). The graph never touches the x-axis.
Step-by-Step Instructions
- Identify 'a': This is the number in front of the x² term. (Note: 'a' cannot be 0).
- Identify 'b': This is the number in front of the x term. Pay attention to negative signs.
- Identify 'c': This is the constant term (the number without an x).
- View Result: The calculator will output the values for x₁ and x₂. If the discriminant is negative, the result will automatically be formatted in complex form (e.g., 2 ± 3i).