Question

Which function represents a function with zeros at -3, -1, 0, and 6?

A. y = (x − 6)(x + 1)(x + 3)
B. y = x(x − 3)(x − 1)(x + 6)
C. y = x(x − 6)(x + 1)(x + 3)
D. y = (x − 3)(x − 1)(x + 6)

Answer 1

Option C

Explanation:

`y = x(x -6)(x +1)(x+3)`

There are four expressions in the above equation, which are multiplying with each other:

1.
`x`

2.
`(x -6)`

3.
`(x + 1)`

4.
`(x + 3)`

The values of x (for which zero y values are obtained) are determined when setting each of the above mentioned expressions equal to 0:

1.
`x = 0`

∴x = 0

2.
`(x - 6) = 0`

∴x = 6

3.
`(x + 1) = 0`

∴x =
`-1`

4.
`(x + 3) = 0`

∴ x =
`-3`

∴The function have zeros at -3, -1, 0 and 6

Function in option C represent the above mentioned characteristics.