Question

What are the zeros of the function?

h(w)=w2+13w+42



Enter your answers in the boxes.

and

Answer 1

To find the zeros of the function \( h(w) = w^2 + 13w + 42 \), we need to solve the equation \( h(w) = 0 \):

\[
w^2 + 13w + 42 = 0
\]

We can factor the quadratic expression. We need two numbers that add up to 13 and multiply to 42. The numbers 6 and 7 satisfy these conditions.

Thus, we can factor the quadratic as follows:

\[
(w + 6)(w + 7) = 0
\]

Now, we set each factor equal to zero to find the zeros of the function:

1. \( w + 6 = 0 \) ⟹ \( w = -6 \)
2. \( w + 7 = 0 \) ⟹ \( w = -7 \)

Therefore, the zeros of the function \( h(w) \) are:

1. \( -6 \)
2. \( -7 \)

So, in the boxes, you would enter:

- First box: \(-6\)
- Second box: \(-7\)