Select the correct answer.
Which function represents a function with zeros at , and 6 ?
A.
B.
C.
D.

Ask by George Ward. in the United States

Mar 30,2025

Question

Select the correct answer.
Which function represents a function with zeros at , and 6 ?
A.
B.
C.
D.

Ask by George Ward. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

Consider a function with zeros at $$ -3 $$, $$ -1 $$, $$ 0 $$, and $$ 6 $$. This means the function must have factors that vanish at these values. The factors corresponding to these zeros are:
$$
(x + 3),\quad (x + 1),\quad x,\quad \text{and}\quad (x - 6).
$$

Thus, a function with these zeros can be written, up to a constant multiple, as:
$$
y = x(x - 6)(x + 1)(x + 3).
$$

Now, we compare with the given options:

- **Option A:** $$ y = (x-6)(x+1)(x+3) $$  
  *This function has zeros at $$6$$, $$-1$$, and $$-3$$, but is missing the zero at $$0$$.*

- **Option B:** $$ y = x(x-3)(x-1)(x+6) $$  
  *This function has zeros at $$0$$, $$3$$, $$1$$, and $$-6$$, which do not match the required zeros.*

- **Option C:** $$ y = x(x-6)(x+1)(x+3) $$  
  *This function has zeros at $$0$$, $$6$$, $$-1$$, and $$-3$$ exactly as required.*

- **Option D:** $$ y = (x-3)(x-1)(x+6) $$  
  *This function has zeros at $$3$$, $$1$$, and $$-6$$, which do not match the required zeros.*

Therefore, the correct answer is:

$$ \textbf{Option C} $$
The correct answer is Option C: $$ y = x(x - 6)(x + 1)(x + 3) $$.

Select the correct answer.
Which function represents a function with zeros at , and 6 ?
A.
B.
C.
D.

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