Quadratic Solver
Solve second-degree equations of the form $ax^2 + bx + c = 0$. This tool calculates real and complex roots using the quadratic formula.
x² +
x +
= 0
First Root ($x_1$)
0
Second Root ($x_2$)
0
Real Roots
The Quadratic Formula
To find the values of $x$, we use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The part under the square root, $b^2 - 4ac$, is called the Discriminant ($D$). If $D$ is positive, you get two real roots. If $D$ is zero, there is one repeated real root. If $D$ is negative, the roots are complex (imaginary numbers).
Frequently Asked Questions
Why can't 'a' be zero? +
If $a = 0$, the $x^2$ term disappears, making it a linear equation ($bx + c = 0$) rather than a quadratic one. The quadratic formula involves dividing by $2a$, and division by zero is impossible.
What does "i" mean in the results? +
The letter i represents an imaginary unit, which is the square root of -1. This happens when the discriminant is negative. These roots are called "Complex Conjugates."
How do I interpret the roots? +
On a graph, the roots are the points where the parabola (the curve of the equation) crosses the x-axis. If the roots are imaginary, the parabola never touches the x-axis.
Can I use decimals for a, b, and c? +
Yes, this calculator accepts both whole numbers and decimals for all coefficients to ensure maximum flexibility for physics or engineering problems.
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