Verified answer

4x^3 – 3x – 1= 0

угадываем корень 1

4*1³ - 3*1 - 1 = 0

4 - 3 - 1 = 0

0 = 0 корень

ищем другие

4x^3 - 4x^2 + 4x^2 -- 4x + x - 1 = 0

4x^2(x - 1) + 4x(x - 1) + (x - 1) = 0

(x - 1)(4x^2 + 4x + 1) = 0

(x - 1)(2x + 1)^2 = 0

x₁ = 1

x₂ = -1/2