Example 18 - Find discriminant of 3x2 - 2x + 1/3 = 0 and - Nature of roots

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Example 18 Find the discriminant of the equation 3x2 โ€“ 2x + 1/3 = 0 and hence find the nature of its roots. Find them, if they are real. 3x2 โ€“ 2x + 1/3=0 (3 ร— 3๐‘ฅ2 โˆ’ 3 ร— 2๐‘ฅ + 1)/3=0 9x2 โ€“ 6x +1 = 0 ร— 3 9x2 โ€“ 6x + 1 = 0 Comparing equation with ax2 + bx + c = 0 a = 9, b = โ€“6 , c = 1 We know that D = b2 โ€“ 4ac D = (โ€“6)2 โ€“ 4 ร— 9 ร— 1 D = 36 โ€“ 36 D = 0 Since D = 0 The given equation has two equal real roots Now using quadratic formula to find roots x = (โˆ’ ๐‘ ยฑ โˆš๐ท)/2๐‘Ž Putting values x = (โˆ’(โˆ’ 6) ยฑ โˆš0)/(2 ร— 9) x = (6 + 0 )/18 x = (6 )/18 x = 1/3 Hence, the roots of the equation are 1/3 , 1/3 .

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