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Question
Find the value of ‘p’, if the following quadratic equation have equal roots:
x2 + (p – 3)x + p = 0
Solution
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
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