We use the method of briot ruffin.
Where,
The possible roots are the 440 splitters divided by the coefficient divisors a.
Divisors of 440 = 440, 220, 110, 88, 55, 44, 40 , 22 , 20 , 11, 10, 8, 5, 4, 2, 1
Testinh the values, We will see:
440 / 55 = 8
This would be one root correct
Then,
x^3 -9x -440 =0
1x^3 + 0x^2 -9x - 440 = 0
1 , 0 , -9 , -440 | 8
Downing the number 1, we stay:
1 , 0 , -9, -440 | 8
, 8 , 64 , 440
1x^2 + 8x + 55 = 0
Ussing the method of baskara
a = 1
b = 8
c = 55
Delta = b^2 - 4ac
Delta = 8^2 - 4.(1).(55)
Delta = 64 - 220
Delta = - 156
To this negative value , Not there is real root.
Then, just x = 8 It is real.
Answer :
X = 8