For the equation $\left|x^2-2x-3\right|=b$, which of the following statements is true?

• Correct answer
  A

  For $b<0$, there are no solutions
• B

  For $b=0$, there are three solutions
• C

  For $0<b<4$, there are two solutions
• D

  For $b=4$, there are four solutions

Solution

$b<0\to \mathrm{n}\mathrm{o }\mathrm{}\mathrm{}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$
$b=0\to \mathrm{t}\mathrm{w}\mathrm{o }\mathrm{}\mathrm{}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$
$0<b<4\to \mathrm{f}\mathrm{o}\mathrm{u}\mathrm{r }\mathrm{}\mathrm{}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$
$b=4\to \mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{e }\mathrm{}\mathrm{}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$

Hence, the correct answer is option: 'A'.