Решите квадратные уравнения с 11 по 20 через дискриминант.

Для решения квадратного уравнения вида $ax^2 + bx + c = 0$ используем формулу дискриминанта $D = b^2 - 4ac$ и корней $x = \frac{-b \pm \sqrt{D}}{2a}$. 11) $x^2 + 10x + 21 = 0$ $D = 10^2 - 4 \cdot 1 \cdot 21 = 100 - 84 = 16$; $\sqrt{D} = 4$ $x_1 = \frac{-10 + 4}{2} = -3$; $x_2 = \frac{-10 - 4}{2} = -7$ 12) $x^2 + 7x + 12 = 0$ $D = 7^2 - 4 \cdot 1 \cdot 12 = 49 - 48 = 1$; $\sqrt{D} = 1$ $x_1 = \frac{-7 + 1}{2} = -3$; $x_2 = \frac{-7 - 1}{2} = -4$ 13) $x^2 + 18x + 65 = 0$ $D = 18^2 - 4 \cdot 1 \cdot 65 = 324 - 260 = 64$; $\sqrt{D} = 8$ $x_1 = \frac{-18 + 8}{2} = -5$; $x_2 = \frac{-18 - 8}{2} = -13$ 14) $x^2 + 22x + 117 = 0$ $D = 22^2 - 4 \cdot 1 \cdot 117 = 484 - 468 = 16$; $\sqrt{D} = 4$ $x_1 = \frac{-22 + 4}{2} = -9$; $x_2 = \frac{-22 - 4}{2} = -13$ 15) $x^2 + 21x + 90 = 0$ $D = 21^2 - 4 \cdot 1 \cdot 90 = 441 - 360 = 81$; $\sqrt{D} = 9$ $x_1 = \frac{-21 + 9}{2} = -6$; $x_2 = \frac{-21 - 9}{2} = -15$ 16) $x^2 + 18x + 77 = 0$ $D = 18^2 - 4 \cdot 1 \cdot 77 = 324 - 308 = 16$; $\sqrt{D} = 4$ $x_1 = \frac{-18 + 4}{2} = -7$; $x_2 = \frac{-18 - 4}{2} = -11$ 17) $x^2 + 16x + 60 = 0$ $D = 16^2 - 4 \cdot 1 \cdot 60 = 256 - 240 = 16$; $\sqrt{D} = 4$ $x_1 = \frac{-16 + 4}{2} = -6$; $x_2 = \frac{-16 - 4}{2} = -10$ 18) $x^2 - 23x + 120 = 0$ $D = (-23)^2 - 4 \cdot 1 \cdot 120 = 529 - 480 = 49$; $\sqrt{D} = 7$ $x_1 = \frac{23 + 7}{2} = 15$; $x_2 = \frac{23 - 7}{2} = 8$ 19) $x^2 + 3x - 40 = 0$ $D = 3^2 - 4 \cdot 1 \cdot (-40) = 9 + 160 = 169$; $\sqrt{D} = 13$ $x_1 = \frac{-3 + 13}{2} = 5$; $x_2 = \frac{-3 - 13}{2} = -8$ 20) $x^2 + 2x - 35 = 0$ $D = 2^2 - 4 \cdot 1 \cdot (-35) = 4 + 140 = 144$; $\sqrt{D} = 12$ $x_1 = \frac{-2 + 12}{2} = 5$; $x_2 = \frac{-2 - 12}{2} = -7$