Instantly find the roots of any quadratic equation ax² + bx + c = 0. Get step-by-step solutions including the discriminant.
Two distinct real roots
A quadratic equation is a polynomial equation of the second degree. The standard form of a quadratic equation is:
Where:
To find the roots (solutions) for x, we use the quadratic formula:
The term inside the square root, b² - 4ac, is called the discriminant (symbol: Δ). It tells us the nature of the roots:
No. If a = 0, the equation becomes a linear equation (bx + c = 0), not a quadratic one. Our calculator will warn you if you input 0 for a.
Currently, this calculator specializes in finding real roots for practical applications. If the discriminant is negative, it will inform you that the roots are complex/imaginary but will not display the imaginary parts.
Sometimes factoring is faster than the formula. You look for two numbers that multiply to ac and add to b. If factoring is difficult, the quadratic formula always works!
