Ex 4.3, 1 (ii) - Chapter 4 Class 10 Quadratic Equations

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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