Question

Найдите корни многочлена:
Р(х) = 8Х3 + 42Х2 + 37Х + 3​

Answer 1

P (x) = 8x³ + 42x² + 37x + 3
0 = 8x³ + 42x² + 37x + 3
0 - 8x³ - 42x² - 37x - 3 =0
-8x³ - 8x² - 34 x² -34x - 3x - 3 = 0
-8x² * (x + 1) - 34x * (x + 1) - 3 (x + 1) = 0
- (x + 1) * (8x² + 34x + 3 ) = 0
(x + 1 ) * (8² + 34x + 3) = 0
8+1 = 0
8x² + 34 x + 3 = 0
x = -1

x₁ = -17 - √265 / 8,
x₂ = -1 ,
x₃ = -17 + √265 / 8