X^3-9x-440=0 (not using factor theorem) and show me how to work it out

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