For ax2+bx+c=0, a=0: the discriminant is D=b2−4ac.
Roots: x1,2=2a−b±D (when D≥0). If D=0 — one (double) root; if D<0 — no real roots.
First rewrite in standard form and read off a,b,c
D>0 — two distinct real roots
D=0 — x=−2ab
Sign of the discriminant
| D | What happens to the roots in R |
|---|---|
| D>0 | Two distinct roots |
| D=0 | One root (multiplicity 2) |
| D<0 | No real roots |
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