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Example 9 Find the discriminant of the equation 3x2 – 2x + 1/3 = 0 and hence find the nature of its roots. Find them, if they are real. 3x2 – 2x + 1/3=0 (3 × 3𝑥2 − 3 × 2𝑥 + 1)/3=0 9x2 – 6x +1 = 0 × 3 9x2 – 6x + 1 = 0 Comparing equation with ax2 + bx + c = 0 a = 9, b = –6 , c = 1 We know that D = b2 – 4ac D = (–6)2 – 4 × 9 × 1 D = 36 – 36 D = 0 Since D = 0 The given equation has two equal real roots Now using quadratic formula to find roots x = (− 𝑏 ± √𝐷)/2𝑎 Putting values x = (−(− 𝟔) ± √𝟎)/(𝟐 × 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo