Quadratic Formula Calculator
Enter the coefficients of any quadratic equation in the form ax² + bx + c = 0 to find its roots, including complex roots when the discriminant is negative.
Show solution steps
Formula
x = (−b ± √(b2 − 4ac)) / 2a
The discriminant b² − 4ac determines the nature of the roots: positive gives two real roots, zero gives one repeated real root, and negative gives two complex roots.
Worked Example
For x² − 3x + 2 = 0 (a=1, b=−3, c=2): discriminant = 1, roots are x=2 and x=1.
How to Use
- Enter the coefficients a, b, and c.
- Read the discriminant and both roots instantly.
- If the discriminant is negative, the roots are shown in complex number form (real u00b1 imaginary i).
Frequently Asked Questions
What if a = 0?
The equation is no longer quadratic (it becomes linear or has no defined solution here), so the calculator flags this rather than dividing by zero.
What does a negative discriminant mean?
It means the equation has no real roots u2014 the parabola never crosses the x-axis. The two roots are complex conjugates, shown in the form a u00b1 bi.
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