Question

What are the zeros of the polynomial function?

f(x)=x2+9x+20

Enter your answers in the boxes.

The zeros of f(x) are
and
.

Answer 1

To find the zeros of the polynomial function \( f(x) = x^2 + 9x + 20 \), we can factor the quadratic expression or use the quadratic formula.

Let's start by factoring.

We need to find two numbers that multiply to \( 20 \) (the constant term) and add up to \( 9 \) (the coefficient of the linear term).

The two numbers that satisfy these conditions are \( 4 \) and \( 5 \), since:

\( 4 \times 5 = 20 \)
\( 4 + 5 = 9 \)

Therefore, we can factor the polynomial as follows:

\[
f(x) = (x + 4)(x + 5)
\]

To find the zeros, we set the factors equal to zero:

1. \( x + 4 = 0 \) → \( x = -4 \)
2. \( x + 5 = 0 \) → \( x = -5 \)

Thus, the zeros of \( f(x) \) are:

-4 and -5.

So, the answers are:

The zeros of f(x) are **-4** and **-5**.