Determine the zeros of the quadratic function y=x2+15x+36

Question

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+
15
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+
36
. (When listing the smaller zero, remember that negative values are always smaller than positive values.)(1 point)
smaller zero: x=
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; greater zero: x=
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Answer 1

To find the zeros of the quadratic function \( y = x^2 + 15x + 36 \), we need to factor the quadratic expression or use the quadratic formula. Let's first try factoring.

We need two numbers that multiply to 36 (the constant term) and add to 15 (the coefficient of the linear term). The numbers that meet these requirements are 3 and 12, since \( 3 \times 12 = 36 \) and \( 3 + 12 = 15 \).

Thus, we can factor the quadratic as follows:

\[ y = (x + 3)(x + 12) \]

To find the zeros, we set \( y = 0 \):

\[ (x + 3)(x + 12) = 0 \]

This gives us two equations:

1. \( x + 3 = 0 \) → \( x = -3 \)
2. \( x + 12 = 0 \) → \( x = -12 \)

Now we have the two zeros:

• Smaller zero: \( x = -12 \)
• Greater zero: \( x = -3 \)

So the answers are:

Smaller zero: \( x = -12 \); Greater zero: \( x = -3 \).