Using x² + 4x = 0, what are the roots of the given equation?

Question 2Answer

a.

\( x = 0,4 \)

b.

\( x = 2,2 \)

c.

\( x = 0,-2 \)

d.

\( x = -2,-2 \)

The given equation is:

\[
x^2 + 4x = 0
\]

We can factor the equation to find its roots.

First, factor out \(x\) from the equation:

\[
x(x + 4) = 0
\]

Now, set each factor equal to zero:

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

So, the roots are \(x = 0\) and \(x = -4\).

The correct answer is not listed in the provided options, but the correct roots should be:

\[
x = 0 \quad \text{and} \quad x = -4
\]

Feel free to ask for any further clarification.

Here are 5 related questions to expand your understanding:
1. How would the equation change if it were \(x^2 + 5x = 0\)?
2. What happens if you add a constant to both sides of the equation?
3. How would you solve \(x^2 + 4x + 4 = 0\)?
4. Can you graph \(x^2 + 4x = 0\) and describe the curve?
5. How does completing the square apply to solving this equation?

**Tip:** Always check if you can factor an equation before using other methods like the quadratic formula.

Using x² + 4x = 0, what are the roots of the given equation?

Discover how to solve the quadratic equation x² + 4x = 0 through factoring. This problem demonstrates key algebraic techniques such as factoring and the Zero Product Property. Suitable for students in Grades 8-10.

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