Find the value of m so that the quadratic equation mx (5x - 6) + 9 = 0 has two equal roots

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  1. Class 10
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Transcript

Question 2 Find the value of ๐‘š so that the quadratic equation ๐‘š๐‘ฅ(5๐‘ฅ โˆ’ 6) + 9 = 0 has two equal roots. Given equation ๐‘š๐‘ฅ(5๐‘ฅ โˆ’ 6) + 9 = 0 5๐‘š๐‘ฅ2 โˆ’ 6๐‘š๐‘ฅ + 9 = 0 Comparing equation with ax2 + bx + c = 0 a = 5๐‘š, b = โ€“6๐‘š, c = 9 Since the equation has 2 equal roots, D = 0 b2 โ€“ 4ac = 0 Putting values (โ€“6๐‘š)2 โ€“ 4 ร— 5๐‘š ร— 9 = 0 36๐‘š2 โ€“ 180๐‘š = 0 6(6๐‘š2 โ€“ 30๐‘š) = 0 6๐‘š2 โ€“ 30๐‘š = 0 6(๐‘š2 โ€“ 5๐‘š) = 0 ๐‘š2 โ€“ 5๐‘š = 0 ๐‘š(๐‘š โˆ’ 5) = 0 Thus, ๐‘š = 0 and ๐‘š = 5 But, if ๐‘š = 0, then the equation would not be a quadratic equation So, ๐‘š = 0 is not possible โˆด Correct answer is ๐‘š = 5

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.