Question

find the zeros of the function f(x).
f(x) = x²(x - 7)(x + 4)
write your answer as a list of values separated by commas.
x =
submit

Explanation:

Step1: Set function to zero

To find the zeros of \( f(x) = x^2(x - 7)(x + 4) \), we set \( f(x) = 0 \), so we have the equation \( x^2(x - 7)(x + 4)=0 \).

Step2: Solve each factor

• For the factor \( x^2 = 0 \), taking the square root of both sides gives \( x = 0 \) (with multiplicity 2, but we still list it as a zero).
• For the factor \( x - 7 = 0 \), adding 7 to both sides gives \( x = 7 \).
• For the factor \( x + 4 = 0 \), subtracting 4 from both sides gives \( x = -4 \).

Answer:

0, 7, -4