# Ex 4.3, 2

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 4.3 ,2 Find the roots of the quadratic equation using quadratic formula (i) 2x2 – 7x + 3 = 0 2x2 – 7x + 3 = 0 Comparing equation with ax2 + bx + c = 0 a = 2, b = – 7, c = 3 We know that D = b2 – 4ac D = ( – 7)2 – 4×2×3 D = ( –7 ×−7)−(4×2×3) D = 49 – 24 D = 25 The roots to equation is given by x = (− 𝑏 ± √𝐷)/2𝑎 Putting values x = (− (− 7) ± √25)/(2 × 2) x = (7 ± √(5^2 ))/4 x = (7 ± 5)/4 Solving Both Hence , the roots to equation are 3 and 1/2 . Ex 4.3 ,2 Find the roots of the quadratic equation using quadratic formula (ii) 2x2 + x – 4 = 0 2x2 + x – 4 = 0 Comparing equation with ax2 + bx + c = 0 a = 2, b = 1, c = – 4 We know that D = b2 – 4ac D = 12 – 4 ×2×−4 D = 1 + 32 = 33 So, the roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (−1 ± √33)/(2 × 2) x = (−1 ± √33)/4 Hence x = (−1 + √33)/4 & x = (−1 − √33)/4 are the roots of the equation Ex 4.3 ,2 Find the roots of the quadratic equation using quadratic formula (iii) 4x2 + 4√3 𝑥+3=0 4x2 + 4√3 𝑥+3=0 Comparing equation with ax2 + bx + c = 0 a = 4, b = 4√3, c = 3 We know that, D = b2 – 4ac D = (4 √3)2 – 4×4×3 D = 4√3×4√3−4×4×3 D = 16 ×3−4×4×3 D = 48 – 48 D = 0 Hence , roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (− (4√3) ± √0)/(2 × 4) x = (−(4√3) )/(2 × 4) x = (−√3)/2 Therefore x = (−√3)/2 & x = (−√3)/2 are the roots of the equation Ex 4.3 ,2 Find the roots of the quadratic equation using quadratic formula (iv) 2x2 + x + 4 = 0 2x2 + x + 4 = 0 Comparing equation with ax2 + bx + c = 0 So, a = 2, b = 1, c = 4 We know that D = b2 – 4ac D = 12 – 4×2×4 D = 1 – 32 D = –31 Hence roots to equation are x = (− 𝑏 ± √𝐷)/2𝑎 Putting values x = (− 1 ± √(−31))/2𝑎 Since there is a negative number in the root, therefore √D will not have any real value. So, there are no real roots for the given equation.

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .