Quadratic formula calculator
Find the roots of x² − 3x + 2 = 0 (x = 1 and x = 2) with the discriminant, including complex roots when it is negative.
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- No upload
- Instant result
Assumptions & formula
Formula and assumptions
D=B²−4AC; x=(−B±√D)/(2A)
Coefficients are normalized by the displayed scale before evaluating roots. The original discriminant equals the normalized discriminant times scale squared. A nonzero original discriminant below the decimal range is shown as a scaled expression, never as zero.
Results
Enter values and press Calculate to see the result here.
How to use this calculator
- Set inputs and units
Enter a, b and c for ax²+bx+c=0, keeping the signs of the coefficients after you move the terms to one side.
- Calculate
Check this worked example: a=1, b=-3, c=2 → Δ=1; roots=2,1; (x−1)(x−2)=0
- Results
Read the discriminant and both roots. A negative discriminant means a complex conjugate pair, not two real crossings.
Questions and limits
What if a is zero?
The equation becomes bx+c=0, and the solver reports its linear or constant outcome instead of dividing by 2a.
Which input errors should I correct?
Don't type x into the coefficient fields. Check inputs where terms nearly cancel, and any precision limit that is reported.
What does this calculation leave out?
The numeric roots describe the polynomial you entered. The decimals shown are not a symbolic proof, and they are not a fit to measured data.