Question

Determine the zeros of quadratic function y = x^2 + 15x + 36

Answer 1

To find the zeros of the quadratic function \( y = x^2 + 15x + 36 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, the coefficients are:
- \( a = 1 \)
- \( b = 15 \)
- \( c = 36 \)

First, we calculate the discriminant (\( b^2 - 4ac \)):

\[
b^2 - 4ac = 15^2 - 4 \cdot 1 \cdot 36
\]
\[
= 225 - 144
\]
\[
= 81
\]

Now that we have the discriminant, we can find the zeros:

\[
x = \frac{-15 \pm \sqrt{81}}{2 \cdot 1}
\]
\[
= \frac{-15 \pm 9}{2}
\]

Now, we will calculate the two possible values for \( x \):

1. Using the positive root:

\[
x = \frac{-15 + 9}{2} = \frac{-6}{2} = -3
\]

2. Using the negative root:

\[
x = \frac{-15 - 9}{2} = \frac{-24}{2} = -12
\]

Thus, the zeros of the quadratic function are:

\[
x = -3 \quad \text{and} \quad x = -12
\]