Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: \(m = 14\)
\(a = m - 12\), \(b = 2(m - 12)\), \(c = 2\)
For real and equal roots, \(b^2 - 4ac = 0\):
\([2(m - 12)]^2 - 4(m - 12)(2) = 0\)
\(4(m - 12)^2 - 8(m - 12) = 0\)
\(4(m - 12)[(m - 12) - 2] = 0\)
\(4(m - 12)(m - 14) = 0\)
\(\therefore m = 12\) or \(m = 14\)
If \(m = 12\), the coefficient of \(x^2\) becomes 0 and the equation is not quadratic (it becomes \(2 = 0\)). So \(m = 12\) is rejected.
\(\therefore m = 14\).