Найти сумму и произведение корней a) x^2+2x-11=0 b) 3x-4x-12=0 c) 4x-9=0 14x-50 Решить: 25X^2=16 5x^2+2x=0 6x^2+7x-3=0 3x^2-11x+15=0

1. a) x² + 2x - 11 = 0;

D = 4 - 4 * 1 * ( - 11) = 4 + 44 = 48>0;

x₁ = ( - 2 - √48) / 2 = ( - 2 - √ (16 * 3)) / 2 = ( - 2 - 4√3) / 2 = 2 ( - 1 - 2√3) / 2 = - 1 - 2√3;

x₂ = ( - 2 + √48) / 2 = - 1 + 2√3.

x₁ + x₂ = - 1 - 2√3 + ( - 1 + 2√3) = - 2;

x₁ * x₂ = ( - 1 - 2√3) ( - 1 + 2√3) = ( - 1) ² - (2√3) ² = 1 - 4 * 3 = 1 - 12 = - 11.

b) 3x - 4x - 12 = 0;

- x - 12 = 0;

- x = 12;

x = - 12.

Уравнение имеет только один корень.

c) 4x - 9 = 0 и 14x - 50 = 0;

4x = 9;

x = 9/4.

14x = 50;

x = 50/14.

x₁ + x₂ = 9/4 + 50/14 = (9 * 7 + 50) / 28 = 113/28.

x₁ * x₂ = 9/4 * 50/14 = 9/2 * 25/14 = 225/28.

2. a) 25x² = 16;

x² = 16/25;

x = ± 4/5.

б) 5x² + 2x = 0;

x (5x + 2) = 0;

x = 0 или 5x + 2 = 0;

5x = - 2;

x = - 2/5.

в) 6x² + 7x - 3 = 0;

D = 49 - 4 * 6 * ( - 3) = 49 + 24 * 3 = 49 + 72 = 121>0;

x₁ = ( - 7 - 11) / 12 = - 18/12 = - 3/2 = - 1 1/2;

x₂ = 4/12 = 1/3.

Ответ: - 1 1/2, 1/3.

с) 3x² - 11x + 15 = 0;

D = 121 - 4 * 3 * 15 = 121 - 180<0.

Нет корней.