1. Найдите сумму и произведение корней уравнения: 1) a) x² - 9x + 12 = 0; б) x² - 16x + 5 = 0; в) у² + бу - 21 = 0; г) 7y - 7 + y² = 0; 2) a) x² - 55x = 0; в) 42z + z² = 0; б) y² - 31 = 0: г) 4,9y - y² = 0; 3) a) 3x² - 17x + 10 = 0; в) 14x - 9x² + 19 = 0; б) 8x² + 21x - 29 = 0; г) 7y² - 12y = 0.

**Теорема Виета** Для квадратного уравнения вида (ax^2 + bx + c = 0), сумма корней (x_1 + x_2 = -rac{b}{a}) и произведение корней (x_1 cdot x_2 = rac{c}{a}). **1) a) (x^2 - 9x + 12 = 0)** (x_1 + x_2 = -rac{-9}{1} = 9) (x_1 cdot x_2 = rac{12}{1} = 12) **1) б) (x^2 - 16x + 5 = 0)** (x_1 + x_2 = -rac{-16}{1} = 16) (x_1 cdot x_2 = rac{5}{1} = 5) **1) в) (y^2 + 6y - 21 = 0)** (y_1 + y_2 = -rac{6}{1} = -6) (y_1 cdot y_2 = rac{-21}{1} = -21) **1) г) (y^2 + 7y - 7 = 0)** (y_1 + y_2 = -rac{7}{1} = -7) (y_1 cdot y_2 = rac{-7}{1} = -7) **2) a) (x^2 - 55x = 0)** (x_1 + x_2 = -rac{-55}{1} = 55) (x_1 cdot x_2 = rac{0}{1} = 0) **2) б) (y^2 - 31 = 0)** (y_1 + y_2 = -rac{0}{1} = 0) (y_1 cdot y_2 = rac{-31}{1} = -31) **2) в) (z^2 + 42 = 0)** (z_1 + z_2 = -rac{0}{1} = 0) (z_1 cdot z_2 = rac{42}{1} = 42) **2) г) (-y^2 + 4.9y = 0) или (y^2 - 4.9y = 0)** (y_1 + y_2 = -rac{-4.9}{1} = 4.9) (y_1 cdot y_2 = rac{0}{1} = 0) **3) a) (3x^2 - 17x + 10 = 0)** (x_1 + x_2 = -rac{-17}{3} = rac{17}{3}) (x_1 cdot x_2 = rac{10}{3}) **3) б) (8x^2 + 21x - 29 = 0)** (x_1 + x_2 = -rac{21}{8}) (x_1 cdot x_2 = rac{-29}{8}) **3) в) (-9x^2 + 14x + 19 = 0) или (9x^2 - 14x - 19 = 0)** (x_1 + x_2 = -rac{-14}{9} = rac{14}{9}) (x_1 cdot x_2 = rac{-19}{9}) **3) г) (7y^2 - 12y = 0)** (y_1 + y_2 = -rac{-12}{7} = rac{12}{7}) (y_1 cdot y_2 = rac{0}{7} = 0)