Question

Consider the quadratic equation x(x-b)=0. Solve this equation. For what value(s) of b are there more than one solution? For what value(s) of is there only one solution? Explain your reasoning.

Answer 1

Given the quadratic equation:

$x(x-b)=0$

Solve for x:

$\begin{gathered} x=0 \\ or,(x-b)=0\rightarrow x=b \end{gathered}$

So, the value of x = {0, b}

Now, the value of b when there is more than one solution will be all the real numbers except zero

So, b = R - {0}

And the value of b when there is only one solution will be: b = {0}