Answer: m = 14
a = m – 12, b = 2(m – 12), c = 2.
For real and equal roots, \(b^2 - 4ac = 0\):
\(4(m-12)^2 - 8(m-12) = 0\)
\(4(m-12)\,[(m-12) - 2] = 0\)
\(4(m-12)(m-14) = 0\), so m = 12 or m = 14.
If m = 12, the coefficient of \(x^2\) is 0 and the equation is not quadratic. Hence m = 14.