Question

which statement is true about the zeros of q(x) = -x(x + 4)(x - 1)?
zeros occur at x = 4, 0, -1
zeros occur at x = -4, -1, 1
zeros occur at x = 0, 1, 4
zeros occur at x = -4, 0, 1

Explanation:

To find the zeros of the function \( q(x) = -x(x + 4)(x - 1) \), we set \( q(x) = 0 \).

Step 1: Set the function equal to zero

We have the equation:
\[
-x(x + 4)(x - 1) = 0
\]

Step 2: Apply the zero - product property

The zero - product property states that if \( a\times b\times c=0 \), then either \( a = 0 \), \( b = 0 \) or \( c = 0 \).

For \( -x(x + 4)(x - 1)=0 \), we consider three cases:

Case 1: \( -x=0 \)

If \( -x = 0 \), then \( x = 0 \).

Case 2: \( x + 4=0 \)

If \( x+4 = 0 \), then \( x=- 4 \).

Case 3: \( x - 1=0 \)

If \( x - 1=0 \), then \( x = 1 \).

So the zeros of the function \( q(x) \) occur at \( x=-4 \), \( x = 0 \) and \( x = 1 \).

Answer:

The statement "Zeros occur at \( x=-4 \), \( 0,1 \)" (the one in the cyan - colored card) is true.