Quadratic Formula Calculator
Solve quadratic equations $ax^2 + bx + c = 0$ with step-by-step solutions, roots, discriminant, and vertex parameters.
Quadratic Equation Solver
Enter the coefficients $a$, $b$, and $c$ to compute real or complex roots.
The Quadratic Formula
For any quadratic equation in standard form $ax^2 + bx + c = 0$ (where $a \neq 0$), the roots $x$ are calculated using the formula:
The term inside the square root, $b^2 - 4ac$, is called the Discriminant ($\Delta$):
- If $\Delta > 0$: Two distinct real roots exist.
- If $\Delta = 0$: Exactly one real root exists (a repeated root).
- If $\Delta < 0$: Two complex (imaginary) conjugate roots exist.
Frequently Asked Questions (FAQs)
It is an automated mathematical solver designed to solve quadratic equations of the form $ax^2 + bx + c = 0$ instantly, generating exact real or complex solutions alongside full step-by-step breakdowns.
If $a = 0$, the equation reduces to a linear equation ($bx + c = 0$). In quadratic equations, $a$ must be non-zero.
When the discriminant ($b^2 - 4ac$) is negative, its square root introduces the imaginary unit $i$ ($\sqrt{-1}$). The result gives conjugate complex roots: $x = p \pm qi$.