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Question
Find the value of ‘p’, if the following quadratic equation have equal roots:
4x2 – (p – 2)x + 1 = 0
Solution
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
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