Q. \(x^2=0\)

Q: Solve x^2=0.

x^2=0 \Rightarrow x=0. Since the only real (and complex) number whose square is zero is 0.

Q: Are there any other solutions in complex numbers for x^2=0?

No. In \mathbb{C}, x^2=0 still implies x=0. Squaring equals zero only at x=0.

Q: Why does x^2=0 imply x=0?

Because x^2= x\cdot x. If x\neq 0, then x\cdot x\neq 0. Contradiction, so x=0.

Q: What is \sqrt{x^2} when x^2=0?

\sqrt{x^2}=|x|. If x^2=0, then x=0, so \sqrt{0}=0.

Q: How do you solve x^2=0 using factoring?

Rewrite as x^2= x\cdot x=0. By the zero product property, x=0.

Q: What is the multiplicity of the root for x^2=0?

The equation x^2=0 has one root x=0 with multiplicity 2.

Q: Can you solve x^2=0 by taking square roots?

Taking square roots gives x=\pm\sqrt{0}. Since \sqrt{0}=0, both signs give x=0.

Answer

\(x^2=0\) means \(x\) squared equals zero. The only real number whose square is zero is \(x=0\).

\[\boxed{x=0}\]

Detailed Explanation

We are asked to solve the equation \(x^2 = 0\).

Step 1: Understand the equation.
We want \(x\) such that when it is squared, the result is \(0\).

Step 2: Use the zero-product idea.
The number \(x^2\) equals \(0\) only when \(x\) itself equals \(0\). This is because squaring preserves the sign in the sense that \(x^2\) cannot be negative, and it becomes \(0\) only at \(x = 0\).

Step 3: Solve for \(x\).
Set \(x = 0\). Then \(x^2 = 0^2 = 0\), which satisfies the equation.

Step 4: State the solution.
The solution is:

\[
x = 0
\]

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Algebra FAQ

Solve \(x^2=0\).

\(x^2=0 \Rightarrow x=0\). Since the only real (and complex) number whose square is zero is \(0\).

Are there any other solutions in complex numbers for \(x^2=0\)?

No. In \(\mathbb{C}\), \(x^2=0\) still implies \(x=0\). Squaring equals zero only at \(x=0\).

Why does \(x^2=0\) imply \(x=0\)?

Because \(x^2= x\cdot x\). If \(x\neq 0\), then \(x\cdot x\neq 0\). Contradiction, so \(x=0\).

What is \( \sqrt{x^2} \) when \(x^2=0\)?

\(\sqrt{x^2}=|x|\). If \(x^2=0\), then \(x=0\), so \(\sqrt{0}=0\).

How do you solve \(x^2=0\) using factoring?

Rewrite as \(x^2= x\cdot x=0\). By the zero product property, \(x=0\).

What is the multiplicity of the root for \(x^2=0\)?

The equation \(x^2=0\) has one root \(x=0\) with multiplicity \(2\).

Can you solve \(x^2=0\) by taking square roots?

Taking square roots gives \(x=\pm\sqrt{0}\). Since \(\sqrt{0}=0\), both signs give \(x=0\).

Solve x²=0 in two steps.
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