Question

explain how 6x^2+18x has multiple soloutions
Answer
give me a similiar problem
Answer
X=-4
X=0
Answered by GPT-4o mini
To determine if the equation \( 6x^2 + 18x = 0 \) has multiple solutions, we can start by factoring out the common factors. Here's how we can break it down:

1. **Factor the equation**:
\[
6x^2 + 18x = 0
\]
We can factor out the common term, which is \( 6x \):
\[
6x(x + 3) = 0
\]

2. **Set each factor to zero**:
Now, we set each factor to zero:
\[
6x = 0 \quad \text{or} \quad x + 3 = 0
\]

3. **Solve for \( x \)**:
- From \( 6x = 0 \):
\[
x = 0
\]
- From \( x + 3 = 0 \):
\[
x = -3
\]

This means the solutions to the equation \( 6x^2 + 18x = 0 \) are \( x = 0 \) and \( x = -3 \). Since we have two distinct solutions, we say that the equation has multiple solutions.

**Summary**: The equation \( 6x^2 + 18x = 0 \) can be factored into \( 6x(x + 3) = 0 \), allowing us to find that the solutions \( x = 0 \) and \( x = -3 \) indicate that the polynomial has multiple solutions.
Answered by GPT-4o mini
Sure! Here’s a similar problem for you to solve:

**Problem**: Find the solutions of the equation \( 4x^2 + 16x = 0 \).

### Instructions:
1. Factor the equation.
2. Set each factor to zero and solve for \( x \).

Let me know if you would like help with solving it!
Answered by GPT-4o mini
That's correct! Let's break down the steps to verify your solutions for the equation \( 4x^2 + 16x = 0 \).

1. **Factor the equation**:
\[
4x^2 + 16x = 0
\]
We can factor out the greatest common factor, which is \( 4x \):
\[
4x(x + 4) = 0
\]

2. **Set each factor to zero**:
Now, we set each factor to zero:
\[
4x = 0 \quad \text{or} \quad x + 4 = 0
\]

3. **Solve for \( x \)**:
- From \( 4x = 0 \):
\[
x = 0
\]
- From \( x + 4 = 0 \):
\[
x = -4
\]

So, the solutions \( x = 0 \) and \( x = -4 \) are indeed correct. Great job! If you would like more problems or further explanations, feel free to ask!