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Formula for the roots of a quadratic equation. Discriminant

For ax2+bx+c=0ax^2+bx+c=0, a0a\neq0: the discriminant is D=b24acD=b^2-4ac. Roots: x1,2=b±D2ax_{1,2}=\frac{-b\pm\sqrt{D}}{2a} (when D0D\ge0). If D=0D=0 — one (double) root; if D<0D<0 — no real roots.
First rewrite in standard form and read off a,b,ca,b,c
D>0D>0 — two distinct real roots
D=0D=0x=b2ax=-\frac{b}{2a}
Sign of the discriminant
DDWhat happens to the roots in R\mathbb{R}
D>0D>0Two distinct roots
D=0D=0One root (multiplicity 2)
D<0D<0No real roots
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