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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 4.3, 1 Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (ii) 3x2 – 4 √3 x + 4 = 0 3x2 – 4√3 x + 4 = 0 Comparing equation with ax2 + bx + c = 0 a = 3, b = – 4√𝟑, c = 4 We know that D = b2 – 4ac D = ( – 4√𝟑 )2 – 4 ×𝟑×𝟒 D = (− 4√3×−4√3)−4×3×4 D = (− 4×− 4×√3×√3)−4×3×4 D = 16 ×3−4×3×4 D = 48 – 48 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 the values x = (−(− 𝟒√𝟑) ± √𝟎)/(𝟐 × 𝟑) x = 4(√3+0)/6 x = 4(√3)/6 x = (𝟐√𝟑)/𝟑 Hence, x = (𝟐√𝟑)/𝟑 & x = (𝟐√𝟑)/𝟑 are the roots of the equation

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.