(m – 12) x2 + 2(m – 12)x + 2 = 0
Comparing the above equation with
ax2 + bx + c = 0, we get
a = m – 12, b = 2(m – 12), c = 2
Since, the roots are real and equal.
∴ ∆ = 0
∴ 4(m – 12) (m – 14) = 0 (m – 12) (m – 14) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ m – 12 = 0 or m – 14 = 0
∴ m = 12 or m = 14
But ,if m = 12, then quadratic coefficient becomes zero.
∴ m ≠ 12
∴ m = 14