Find m if (m – 12)x² + 2(m – 12)x + 2 = 0 has real and equal roots.

For roots to be equal, determinant must be equal to 0.

in case of quadratic eq., ax² + bx + c = 0

determinant(D) = b² – 4ac

According to the question,

a = m – 12

⇒ b = 2(m – 12)

⇒ c = 2

So, 4(m – 12)² – 4(m – 12)x2 = D

⇒ 4(m² + 144 – 24m) – 8(m – 12) = 0

⇒ 4m² + 576 – 96m – 8m + 96 = 0

⇒ 4m² – 104m + 672 = 0

⇒ m² – 26m + 168 = 0

⇒ m² – 12m – 14m + 168 = 0

⇒ m(m – 12) – 14(m – 12) = 0

⇒ (m – 12)(m – 14) = 0

⇒ m = 12 or m = 14