Trinomul patrat

1. Ecuatia patrata ax^{2} + bx + c = 0, a ≠ 0 are

a) doua solutii distincte, daca Δ = b^{2} − 4ac > 0

x_{1} = \frac{−b − \sqrt{Δ}}{2a}, x_{2} = \frac{−b + \sqrt{Δ}}{2a};

b) doua radacini egale, daca Δ = 0, x_{1} = x_{2} = −\frac{b}{2a};

c) nu are solutii, daca Δ < 0.

Cazuri particulare

1. ax^{2} + 2kx + c = 0, a ≠ 0, x_{1,2} = \frac{−k ± \sqrt{k^{2} − ac}}{a} (k^{2} − ac ≥ 0).

2. x^{2} + px + q = 0, x_{1,2} = −\frac{p}{2} ± \sqrt{(\frac{p}{2})^{2} − q}, daca p^{2} ≥ 4q.

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