Quadratic Equation Solver

Check your algebra homework instantly with our Quadratic Equation Solver. Enter your $a$, $b$, and $c$ coefficients to find the exact roots, the discriminant, and whether the roots are real or complex.

The Quadratic Formula

A standard quadratic equation is written in the form:

$ax^2 + bx + c = 0$

To find the roots (the points where the parabola crosses the x-axis), we use the famous quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The Discriminant ($\Delta$)

The part of the formula under the square root is called the discriminant. It tells you exactly what kind of roots the equation has:

$\Delta = b^2 - 4ac$

Understanding the Results

By analyzing the discriminant ($\Delta$), you can check if your homework answers make sense:

• If $\Delta > 0$: The equation has two distinct real roots. The parabola crosses the x-axis at two different points.
• If $\Delta = 0$: The equation has one repeated real root. The vertex of the parabola rests exactly on the x-axis.
• If $\Delta < 0$: The equation has two complex (imaginary) roots. The parabola never touches the x-axis. Complex roots are usually written in the format $a + bi$.