Answer:
A
Step-by-step 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:
\(x^{2}-3=0\\x^{2}=3\\x=\sqrt{3} , -\sqrt{3}\)
- Solving second one, we have:
\(x-5=0\\x=5\)
Thus three zeros of the function are \(\sqrt{3}\) , \(-\sqrt{3}\) , and \(5\)
Answer choice A is right.
