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Kvadratická nerovnice

Kalkulačka

Zvolte typ nerovnice

ax2 + bx + c > 0
ax2 + bx + c ≥ 0
ax2 + bx + c < 0
ax2 + bx + c ≤ 0

Zadejte nerovnici

 x2 +   x +   > 
+

Příklad:

 x2 +   x +   > 
$$ x^2 - 5,3x \gt \frac{3}{7} $$
Zaokrouhlit na desetinné místo

Vzorce

$$ \boxed{ax^2 + bx + c \gt 0} $$
$$ \underline{\underline{\bullet \ a \neq 0}} $$
$$ \boxed{D = b^2 - 4\cdot a c} $$
$$ \underline{\underline{\circ \ D \gt 0}} $$
$$ x_{1,2} = \frac{-b \pm \sqrt{D}}{2\cdot a} $$
$$ x_1 \lt x_2 $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ x_1 \right) \cup \left(x_2;\ +\infty\right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(x_1;\ x_2 \right) $$
$$ \underline{\underline{\circ \ D = 0}} $$
$$ x_1 = x_2 = \frac{-b}{2\cdot a} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ x_1 \right) \cup \left(x_1;\ +\infty\right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\underline{\circ \ D \lt 0}} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\underline{\bullet \ a = 0}} $$
○ lineární nerovnice
$$ \boxed{ax^2 + bx + c \ge 0} $$
$$ \underline{\underline{\bullet \ a \neq 0}} $$
$$ \boxed{D = b^2 - 4\cdot a c} $$
$$ \underline{\underline{\circ \ D \gt 0}} $$
$$ x_{1,2} = \frac{-b \pm \sqrt{D}}{2\cdot a} $$
$$ x_1 \lt x_2 $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ x_1 \right\rangle \cup \left\langle x_2;\ +\infty\right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left\langle x_1;\ x_2 \right\rangle $$
$$ \underline{\underline{\circ \ D = 0}} $$
$$ x_1 = x_2 = \frac{-b}{2\cdot a} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x = \left\{x_1 \right\} $$
$$ \underline{\underline{\circ \ D \lt 0}} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\underline{\bullet \ a = 0}} $$
○ lineární nerovnice
$$ \boxed{ax^2 + bx + c \lt 0} $$
$$ \underline{\underline{\bullet \ a \neq 0}} $$
$$ \boxed{D = b^2 - 4\cdot a c} $$
$$ \underline{\underline{\circ \ D \gt 0}} $$
$$ x_{1,2} = \frac{-b \pm \sqrt{D}}{2\cdot a} $$
$$ x_1 \lt x_2 $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left(x_1;\ x_2 \right) $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ x_1 \right) \cup \left(x_2;\ +\infty\right) $$
$$ \underline{\underline{\circ \ D = 0}} $$
$$ x_1 = x_2 = \frac{-b}{2\cdot a} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ x_1 \right) \cup \left(x_1;\ +\infty\right) $$
$$ \underline{\underline{\circ \ D \lt 0}} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\underline{\bullet \ a = 0}} $$
○ lineární nerovnice
$$ \boxed{ax^2 + bx + c \le 0} $$
$$ \underline{\underline{\bullet \ a \neq 0}} $$
$$ \boxed{D = b^2 - 4\cdot a c} $$
$$ \underline{\underline{\circ \ D \gt 0}} $$
$$ x_{1,2} = \frac{-b \pm \sqrt{D}}{2\cdot a} $$
$$ x_1 \lt x_2 $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x \in \left\langle x_1;\ x_2 \right\rangle $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ x_1 \right\rangle \cup \left\langle x_2;\ +\infty\right) $$
$$ \underline{\underline{\circ \ D = 0}} $$
$$ x_1 = x_2 = \frac{-b}{2\cdot a} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x = \left\{x_1 \right\} $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\underline{\circ \ D \lt 0}} $$
$$ \underline{\bullet \ a \gt 0} $$
$$ x = \left\{\right\} $$
$$ \underline{\bullet \ a \lt 0} $$
$$ x \in \left(-\infty;\ +\infty \right) $$
$$ \underline{\underline{\bullet \ a = 0}} $$
○ lineární nerovnice

Uživatelské hodnocení

4,6/5 (10×)