Question

find the zeros of the function f(x).
f(x) = x²(x + 3)
write your answer as a list of values separated by commas.
x =
submit

Explanation:

Step1: Set function to zero

To find the zeros of \( f(x) = x^2(x + 3) \), we set \( f(x) = 0 \), so we have the equation \( x^2(x + 3)=0 \).

Step2: Apply zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). For the equation \( x^2(x + 3)=0 \), we consider two cases:

• Case 1: \( x^2=0 \). Taking the square root of both sides, we get \( x = 0 \) (with multiplicity 2).
• Case 2: \( x+3 = 0 \). Solving for \( x \), we subtract 3 from both sides of the equation, and we get \( x=-3 \).

Answer:

0, - 3