Question

Use the factored form and the zero product property to solve (find the zeros) 5x^2 + 18x = 0

Answer 1

To find the zeros of the equation \( 5x^2 + 18x = 0 \), we can start by factoring the expression.

1. **Factor out the common term**:
\[
5x^2 + 18x = 0
\]
Both terms contain \( x \), so we can factor it out:
\[
x(5x + 18) = 0
\]

2. **Apply the Zero Product Property**:
The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must be zero. This gives us two equations to solve:
\[
x = 0
\]
and
\[
5x + 18 = 0
\]

3. **Solve the second equation**:
\[
5x + 18 = 0
\]
Subtract 18 from both sides:
\[
5x = -18
\]
Now, divide by 5:
\[
x = -\frac{18}{5}
\]

4. **Summarize the solutions**:
The solutions (or zeros) of the equation \( 5x^2 + 18x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{18}{5}
\]

Thus, the zeros of the equation are \( x = 0 \) and \( x = -\frac{18}{5} \).