Question

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:

x² – (m + 2)x + (m + 5) = 0

Answer 1

x² – (m + 2)x + (m + 5) = 0

Here a = 1, b = – 4(m + 2) and c = m + 5

Given equation has equal roots

Then D = 0

`=>` b² – 4ac = 0

`=>` [–(m + 2)]² – 4(1)(m + 5) = 0

`=>` m² + 4m + 4 – 4m – 20 = 0 

`=>` m² – 16 = 0

`=>` m² = 16

`=>` m = ±4 

Put value of m in given equation

x² – 6x + 9 = 0 or x² + 2x + 1 = 0

`=>` (x – 3)² = 0 or (x + 1)² = 0

`=>` x – 3 = 0 or x + 1 = 0

`=>` x = 3 or x = –1