Question

What are the zeros of f(x) = (x - 5)(x - 4)(x - 2)?

O5, -4,2
O 5, -4,-2
O 5, 4,2
O 5, 4, -2

Answer 1

The zeros of f(x) are:

`x=5,\:x=4,\:x=2`

Explanation:

Given the expression

`f\left(x\right)\:=\:\left(x\:-\:5\right)\left(x\:-\:4\right)\left(x\:-\:2\right)`

substituting f(x) = 0 to determine zeros of f(x)

`0\:=\:\left(x\:-\:5\right)\left(x\:-\:4\right)\left(x\:-\:2\right)`

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

`x-5=0\quad \mathrm{or}\quad \:x-4=0\quad \mathrm{or}\quad \:x-2=0`

solving x-5=0

`x-5=0`

adding 5 to both sides

`x-5+5 = 0+5`

`x = 5`

solving x-4=0

`x-4=0`

adding 4 to both sides

`x-4+4 = 0+4`

`x = 4`

solving x-2=0

`x-2=0`

adding 2 to both sides

`x-2+2 = 0+2`

`x = 2`

Therefore, the zeros of f(x) are:

`x=5,\:x=4,\:x=2`