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Question
Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Solution
Given quadratic equation is
px(x – 2) + 6 = 0
`\implies` px2 – 2px + 6 = 0
For two equal and real roots
(Discriminant) D = 0
`\implies` b2 – 4ac = 0
Here, b = –2p, a = p, c = 6
∴ (–2p)2 – 4 × p × 6 = 0
`\implies` 4p2 – 24p = 0
`\implies` 4p(p – 6) = 0
`\implies` p = 6
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