Question

Find the value of ‘m’, if the following equation has equal roots:

(m – 2)x² – (5 + m)x + 16 = 0

Answer 1

(m – 2)x² – (5 + m)x + 16 = 0

Here a = m – 2, b = –(5 + m) and c = 16

Given: Equation has equal roots

Then D = 0

`\implies` b² – 4ac = 0

`\implies` [–(5 + m)]² – 4(m – 2)(16) = 0

`\implies` 25 + m² + 10m –  64m + 128 = 0

`\implies` m² – 54m + 153 = 0

`\implies` m² – 51m – 3m + 153 = 0

`\implies` m(m – 51) – 3(m – 51) = 0

`\implies` (m – 51)(m – 3) = 0

Then m – 51 = 0 or m – 3 = 0

`\implies` m = 51 or m = 3