Let the function #h# be defined by # h(x)=12 + x^2/4#. If #h(2m) = 8m#, what is one possible value of m?

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Answer 1 · 2017-01-14T22:42:47

The only possible values for #m# are #2# and #6#.

Using the formula of #h#, we get that for any real #m#,

#h(2m) = 12 + (4m^2)/4 = 12 + m^2#.

#h(2m) = 8m# now becomes:

#12 + m^2 = 8m => m^2 - 8m + 12 = 0#

The discriminant is: #D = 8^2 - 4 * 1 * 12 = 16 > 0#
The roots of this equation are, using the quadratic formula:

#(8 +- sqrt(16))/2# , so #m# can take either the value #2# or #6#.

Both #2# and #6# are acceptable answers.