solve 27x^3+54x^2+198x-73=0

Question

Solve this equation

Answer 1

X→ y-54/3×27 ( Gardano/Tartaglia)

Answer 2

The given becomes y^3+6y-7=0

Answer 3

Sum of coefficients: zero

Answer 4

Then y,=1→x,=1/3

Answer 5

Therefore the given can be written as (3x-1)•(9x^2+21x+73)=0

Answer 6

Solving the quadratic we get the other two solutions -7/6± I 3/2|√3|

Answer 7

27x³+54x²+198x-73=(3x-1)(9x²+21x+73).

Using synthetic division for the zero x=1/3:

1/3 | 27 54 198 | -73

        27  9    21 |  73

        27 63 219 |   0 = 3(9x²+21x+73).

9x²+21x+73=0 can be solved using the quadratic formula.

x=(-21±√(441-2628))/18=(-21±27i√3)/18=(-7±9i√3)/6.

Zeroes are 1/3, (-7+9√3)/6, (-7-9√3)/6.