Let's use the mirror equation to solve the problem:
[tex] \frac{1}{f}= \frac{1}{d_o}+ \frac{1}{d_i} [/tex]
where f is the focal length of the mirror, [tex]d_o[/tex] the distance of the object from the mirror, and [tex]d_i[/tex] the distance of the image from the mirror.
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for [tex]d_i[/tex] by using the numbers given in the text of the problem:
[tex] \frac{1}{12 cm}= \frac{1}{5 cm}+ \frac{1}{d_i} [/tex]
[tex] \frac{1}{d_i}= -\frac{7}{60 cm} [/tex]
[tex]d_i = -8.6 cm[/tex]
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.
