Question

Find the value of ‘p’, if the following quadratic equation have equal roots:

4x² – (p – 2)x + 1 = 0

Answer 1

4x² – (p – 2)x + 1 = 0

Here a = 4, b = – (p – 2) and c = 1

Given: equation has equal roots

Then d = 0

`=>` b² – 4ac = 0

`=>` [–(p – 2)]² – 4(4)(1) = 0

`=>` p² + 4 – 4p – 16 = 0

`=>` p² – 4p – 12 = 0

`=>` p² – 6p + 2p – 12 = 0

`=>` p(p – 6)(p – 6) = 0

`=>` (p – 6)(p + 2) = 0

Then p – 6 = 0 or p + 2 = 0

`=>` p = 6 or p = –2