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What are the zeros of the function?

h(w)=w2+13w+42



Enter your answers in the boxes.

and

1 answer

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: \(-7\)