Answer:
A
Step-by-step explanation:
To find the zeros of the function given, we set [tex]f(x)=0[/tex]. We have:
[tex]x^{3}-5x^{2}-3x+15=0[/tex]
We group first two terms together and last two terms together. Then we take common terms and combine.
[tex](x^{3}-5x^{2})+(-3x+15)=0\\x^{2}(x-5)-3(x-5)=0\\(x^{2}-3)(x-5)=0[/tex]
Here, EITHER [tex]x^{2}-3=0[/tex] OR [tex]x-5=0[/tex]
- Solving first one, we have:
[tex]x^{2}-3=0\\x^{2}=3\\x=\sqrt{3} , -\sqrt{3}[/tex]
- Solving second one, we have:
[tex]x-5=0\\x=5[/tex]
Thus three zeros of the function are [tex]\sqrt{3}[/tex] , [tex]-\sqrt{3}[/tex] , and [tex]5[/tex]
Answer choice A is right.
