Решите уравнение:
а) 2x^3 + 7x^2 + 2x - 3 = 0
б) x^4 - x^3 - 7x^2 + x + 6 = 0

1) 2x³ + 7x² + 2x - 3 = 0

(2x³ + 2x²) + (5x² + 5x) - (3x + 3)= 0

2x² (x + 1) + 5x(x + 1) - 3(x + 1) = 0

(x + 1)(2x² + 5x - 3) = 0

x + 1 = 0

x₁ = - 1

2x² + 5x - 3 = 0

D= 5² - 4 * 2 * (- 3) = 25 + 24 = 49 = 7²

x₂ = (- 5 - 7)/4 = - 3

x₃ = (- 5 + 7)/4 = 0,5

ответ : - 3 ; - 1 ; 0,5

2) x⁴ - x³ - 7x² + x + 6 = 0

(x⁴ - x³) - (6x² - 6) - (x² - x) = 0

x³(x - 1) - 6(x² - 1) - x(x - 1) = 0

x³ (x - 1) - 6(x - 1)(x + 1) - x(x - 1) = 0

(x - 1)(x³ - 6x - 6 - x) = 0

(x - 1)(x³ - 7x - 6) = 0

x - 1 = 0

x₁ = 1

x³ - 7x - 6 = 0

(x³ - x) - (6x + 6) = 0

x(x² - 1) - 6(x + 1) = 0

x(x + 1)(x - 1) - 6(x + 1) = 0

(x + 1)(x² - x - 6) = 0

x + 1 = 0

x₂ = - 1

x² - x - 6 = 0

x₃ = - 2

x₄ = 3

ответ : - 2 ; - 1 ; 1 ; 3