Question

What are the real zeroes

Answer 1

You have to plug the values in the expression and see if it returns zero.

The only points where the function evaluates to zero are
`x=\pm 3` and
`x=6`

Answer 2

ANSWER

B. -3,3,-6

Step-by-step explanation

We equate the given polynomial to zero.


`{x}^(3) + 6 {x}^(2) - 9x - 54 = 0`

Factor by grouping;


`{x}^(2) (x + 6) - 9(x + 6) = 0`

Factor further;


`( {x}^(2) - 9)(x + 6) = 0`

Either


`{x}^(2) - 9 = 0 \: or \: x + 6 = 0`


`{x}^(2) = 9 \: or \: x = - 6`


`x = \pm √(9) \: or \: x = - 6`


`x = \pm 3 \: or \: x = - 6`

The zeroes are

x=3,-3,-6