Question: The smallest value of $x$ in the quadratic equation $$x^2 - 3x = 0$$ is which of the following?
A
3
B
-3
C
0
D
\sqrt{3}
E
-\sqrt{3}
1. **State the problem:** Find the smallest value of $x$ that satisfies the quadratic equation $$x^2 - 3x = 0$$.
2. **Write the equation:** $$x^2 - 3x = 0$$.
3. **Factor the equation:** Factor out the common factor $x$:
$$x(x - 3) = 0$$
4. **Apply the zero product property:** For the product to be zero, either
$$x = 0$$
or
$$x - 3 = 0 \implies x = 3$$
5. **Identify the smallest value:** The solutions are $x = 0$ and $x = 3$. Among these, the smallest value is
$$\boxed{0}$$.
6. **Check the options:** Option C corresponds to $0$, so the answer is C.