Question

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

x² + (p – 3)x + p = 0

Answer 1

x² + (p – 3)x + p = 0

Here a = 1, b = (p – 3), c = p

Since the roots are equal

`=>` b² – 4ac = 0

`=>` (p – 3)² – 4(1)(p) = 0

`=>` p² + 9 – 6p – 4p = 0

`=>` p² – 10p + 9 = 0

`=>` p(p – 9) – 1(p – 9) = 0

`=>` (p – 9)(p – 1) = 0

`=>` p – 9 = 0 or p – 1 = 0

`=>` p = 9 or p = 1