Question

Which of the following represents the zeros of f(x) = x3 − 5x2 − 3x + 15?

a. 5, √3, -√3
b.-5, -√3, -√3
c.5, -√3, -√3
d-5, √3, √3

Answer 1

Hello,

Answer A

x^3-5x²-3x+15=x^2(x-5)-3(x-5)
=(x-5)(x^2-3)
=(x-5)(x+√3)(x-√3)

Answer 2

A

Explanation:

To find the zeros of the function given, we set
`f(x)=0`. We have:

`x^(3)-5x^(2)-3x+15=0`

We group first two terms together and last two terms together. Then we take common terms and combine.

`(x^(3)-5x^(2))+(-3x+15)=0\\x^(2)(x-5)-3(x-5)=0\\(x^(2)-3)(x-5)=0`

Here, EITHER
`x^(2)-3=0` OR
`x-5=0`

• Solving first one, we have:

`x^(2)-3=0\\x^(2)=3\\x=√(3) , -√(3)`

• Solving second one, we have:

`x-5=0\\x=5`

Thus three zeros of the function are
`√(3)` ,
`-√(3)` , and
`5`

Answer choice A is right.