Answer:
4 roots: 2 , -3, 1+√2, 1 - √2
Step-by-step explanation:
x⁴ − x³ − 9x² + 11x + 6 = 0 leading: 1 (x⁴) Trailing: 6 (1,2,3,6)
possible roots: trailing/leading (±1 , ±2, ±3, ±6)
Test: x = 2 (2)⁴ - (2)³ - 9*(2)² + 11*(2) + 6 = 0
x = -3 (-3)⁴ - (-3)³ - 9*(-3)² + 11*(-3) + 6 = 0
By rational roots test: possible roots (x-2)(x+3) are factors
Long division: (x⁴ − x³ − 9x² + 11x + 6) / (x-2)(x+3) = x²-2x-1
roots of x²-2x-1: x= (-b±√b²-4ac) / 2a
x = (2 ± √4+4) / 2 = (2 ± 2√2) / 2 = 1 ± √2
