I encountered a Math problem that I don't quite understand.
For what value of $b$ does the equation $ba^2 + 2a - 3 = 0$ have a single solution for $a$?
My reasoning is that both $-1/3$ and $0$ are correct answers, but $-1/3$ is apparently wrong (according to the answer key), despite making the equation have a single solution.
People told me that $-1/3$ will make the equation have a "double" solution and not a "single" solution. But is there actually something called a "double" solution?
A solution is a "value" that satisfies an equation. It is different from a root. $-1/3$ will make the equation have one "value" that satisfies it: $3$.
People told me that because the question asked for a "single" solution, it implies that the graph crosses (not just touches) the $x$-axis at $0$. They told me that "single" is different from "one" solution. But that is not really a function here. When I graph it, it is a vertical line. It is just an equation, and I don't think "single" is different from "one" solution. It is just a value. It has nothing to do with "roots".
Please clarify which of the opinions is correct and why.